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1. Do the Math: Secrets, Lies, and Algebra by Wendy Lichtman | |
Hardcover: 192
Pages
(2007-07-01)
list price: US$16.99 -- used & new: US$6.60 (price subject to change: see help) Asin: B003NHR9CY Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In the eighth grade, 1 math whiz < 1 popular boy, according to Tess's calculations. That is, until she has to factor in a few more variables, like: Then there's the suspicious guy Tess's parents know, but that's a whole different problem. Can Tess find the solutions? Customer Reviews (17)
mystery and math
More gimmick than tale.
Inappropriate for 9 year olds!
Reading AND Math are cool in Middle School
A fun read |
2. Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore | |
Paperback: 608
Pages
(2006-01-04)
list price: US$29.95 -- used & new: US$18.68 (price subject to change: see help) Asin: 0486445291 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in expressing concepts and results from several fields of physics. 1974 edition. Includes 75 figures and 17 tables. Customer Reviews (8)
Lie groups, not just for particle physics
Not fair on non-physicist mathematicians
Lie groups, examples and exercises
This book becomes my reference on group theory in physics
Rave Review |
3. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Brian C. Hall | |
Hardcover: 250
Pages
(2003-08-07)
list price: US$64.95 -- used & new: US$36.82 (price subject to change: see help) Asin: 0387401229 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The text is divided into two parts. The first covers Lie groupsand Lie algebras and the relationship between them, along withbasic representation theory. The second part covers the theory ofsemisimple Lie groups and Lie algebras, beginning with a detailedanalysis of the representations of SU(3). The author illustratesthe general theory with numerous images pertaining to Liealgebras of rank two and rank three, including images of rootsystems, lattices of dominant integral weights, and weightdiagrams. This book is sure to become a standard textbook forgraduate students in mathematics and physics with little or noprior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at theUniversity of Notre Dame. Customer Reviews (8)
Abominable formatting
Distracting focus on examples
Lie Groups on Kindle
Excellent introduction into the theory of Lie Groups
Horrible |
4. Lie Algebras by Nathan Jacobson | |
Paperback: 331
Pages
(1979-12-01)
list price: US$15.95 -- used & new: US$8.00 (price subject to change: see help) Asin: 0486638324 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A Gem from The Past |
5. Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics) (v. 9) by J.E. Humphreys | |
Hardcover: 196
Pages
(1973-01-23)
list price: US$69.95 -- used & new: US$49.00 (price subject to change: see help) Asin: 0387900535 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
It's so good l, I covet to have written it myself!
a good text
dense and uninviting
There is a lot here for such a short book The first chapter covers the basic definitions of Lie algebras and the algebraic properties of Lie algebras. No historical motivation is given, such as the connection of the theory with Lie groups, and Lie algebras are defined as vector spaces over fields, and not in the general setting of modules over a commutative ring. The four classical Lie algebras are defined, namely the special linear, symplectic, and orthogonal algebras. The physicist reader should pay attention to the (short) discussion on Lie algebras of derivations, given its connection to the adjoint representation and its importance in applications. The important notions of solvability and nilpotency are covered in fairly good detail. Engel's theorem, which essentially says that if all elements of a Lie algebra are nilpotent under the 'bracket", then the Lie algebra itself is nilpotent, is proven. The second chapter gives more into the structure of semisimple Lie algebras with the first result being the solution of the "eigenvalue" problem for solvable subalgebras of gl(V), where V is finite-dimensional. Cartan's criterion, giving conditions for the solvability of a Lie algebra, is proven, along with the criterion of semisimplicity using the Killing form. The representation theory of Lie algebras is begun in this chapter, with proof of Weyl's theorem. This theorem is essentially a generalization to Lie algebras of a similar result from elementary linear algebra, namely the Jordan decomposition of matrices. Again, physicist readers should pay close attention to the details of the discussion on root space decompositions. This is followed in chapter 3 by an in-depth treatment of root systems, wherein a positive-definite symmetric bilinear form is chosen on a fixed Euclidean space. These root systems enable a more transparent approach to the representation theory of Lie algebras. The theory of weights along with the Weyl group, allow a description of the representation theory that depends only on the root system. In addition, one can prove that two semisimple Lie algebras with the same root system are isomorphic, as is done in the next chapter. More precisely, it is shown that a semisimple Lie algebra and a maximal toral subalgebra is determined up to isomorphism by its root system. These maximal toral subalgebras are conjugate under the automorphisms of the Lie algebra. The author further shows that for an arbitary Lie algebra that is true, if one replaces the maximal toral subalgebra by a Cartan subalgebra. The proofs given do not use algebraic geometry, and so they are more accessible to beginning students. In chapter 5, the author introduces the universal enveloping algebra, and proves the Poincare-Birkhoff-Witt theorem. The goal of the author is to find a presentation of a semisimple Lie algebra over a field of characteristic 0 by generators and relations which depend only on the root system. This will show that a semisimple Lie algebra is completely determined by its root system (even if it is infinite dimensional). Chapter 6 is very demanding, and will require a lot of time to get through for the newcomer to the representation theory of Lie algebras. Weight spaces and maximal vectors are introduced in the context of modules over semisimple Lie algebras L. Finite dimensional irreducible L-modules are studied by first considering L-modules generated by a maximal vector. It is shown that if two standard cyclic modules of highest weight are irreducible, then they are isomorphic. The existence of a finite dimensional irreducible standard cyclic module is shown. Freudenthal's formula, which gives a formula for the multiplicity of an element of an irreducible L-module of heighest weight, is proven. A consideration of characters on infinite-dimensional modules leads to a proof of Weyl's formulas on characters of finite dimensional modules. The last chapter of the book considers Chevelley algebras and groups. Their introduction is done in the context of constructing irreducible integral representations of semisimple Lie algebras.
Excellent Introduction to Lie Algebras Highly recommended; every mathematician should knowthe basics of Lie algebras. ... Read more |
6. Representations of Semisimple Lie Algebras in the BGG Category $\mathscr {O}$ (Graduate Studies in Mathematics) by James E. Humphreys | |
Hardcover: 289
Pages
(2008-07-22)
list price: US$59.00 -- used & new: US$39.82 (price subject to change: see help) Asin: 0821846787 Canada | United Kingdom | Germany | France | Japan | |
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7. Introduction to Lie Algebras (Springer Undergraduate Mathematics Series) by Karin Erdmann, Mark J. Wildon | |
Paperback: 254
Pages
(2006-04-04)
list price: US$49.95 -- used & new: US$30.60 (price subject to change: see help) Asin: 1846280400 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics. Customer Reviews (1)
Wonderful Introduction |
8. Complex Semisimple Lie Algebras by Jean-Pierre Serre | |
Hardcover: 83
Pages
(2001-01-25)
list price: US$59.95 -- used & new: US$24.98 (price subject to change: see help) Asin: 3540678271 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
An encyclopedia
One of the most valuable expositions in Lie-theory |
9. Semi-Simple Lie Algebras and Their Representations (Dover Books on Mathematics) by Robert N. Cahn | |
Paperback: 176
Pages
(2006-03-17)
list price: US$12.95 -- used & new: US$7.50 (price subject to change: see help) Asin: 0486449998 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Subjects include simple roots and the Cartan matrix, the classical and exceptional Lie algebras, the Weyl group, and more. 1984 edition. Customer Reviews (4)
A small book with a big Kernal
A practical guide to Lie algebras and representations
A pleasant read In chapter 1 the author begins the study of SU(2), the group of unitary 2 x 2 matrices of determinant 1. He does this by first considering the matrix representations of infinitesimal rotations in 3-dimenensional space. "Exponentiating" these matrices gives the finite rotational matrices. He then shows that the consideration of products of finite rotations involves knowledge of the commutators of the infinitesimal rotations. Viewing these commutators abstractly motivates the definition of a Lie algebra. He then shows that the rotation matrices form a (3-dimensional) 'representation' of the Lie algebra. Higher-dimensional representations he shows can be obtained by analogies to what is done in quantum mechanics, via the addition of angular momentum and are parametrized by spin (denoted j). The representation of smallest dimension is given by j = 1/2 and corresponds to SU(2). He is careful to point out that the rotations in 3 dimensions and SU(2) have the same Lie algebra but are not the same group. The constructions in chapter 1, particularly the concept of "exponentiating", are central to the understanding of Lie algebras in general. This is readily apparent in the next chapter wherein he studies the Lie algebra of SU(3), the 3x3 unitary matrices of determinant 1. SU(3) has to rank as one of the most important groups in elementary particle physics. The (abstract) Lie algebra corresponding to the commutation relations of this group have various representations, the 8-dimensional, or "adjoint" representation being one of great interest. The author finds the famous 'Cartan subalgebra' of the Lie algebra, shows that it 2-dimensional and Abelian, and how eigenvectors of the adjoint operator can form a basis for the Lie algebra, as long as this operator corrresponds to an element of the Cartan subalgebra. Further, he shows that the eigenvalues of this operator depend linearly on this element, and then defines functionals on the Cartan subalgebra, called the roots, and they form the dual space to the Lie algebra. Dual spaces are familiar to physicists in the Dirac bra-ket formalism. The geometry of Lie algebras is very well understood and is formulated in terms of the roots of the algebra and a kind of scalar product (except is not positive definite) for the Lie algebra called the 'Killing form'. The Killing form is defined on the root space, and gives a correspondence between the Cartan subalgebra and its dual. The author then shows how to use the Killing form to obtain a scalar product on the root space, and this scalar product illustrates more clearly the symmetry of the Lie algebra. The property of being semisimple is then defined abstractly by the author, namely a Lie algebra with no Abelian ideals. He states, but does not prove entirely, that the Killing form is non-degenerate if and only if the Lie algebra is semisimple. The treatment becomes more abstract in chapter 4, wherein the author studies the structure of simple Lie algebras, since every semisimple algebra can be written as the sum of simple Lie algebras. The author shows how to obtain the Cartan subalgebra in general, motivating his procedures with what is done for SU(3). He also proves the invariance of the Lie algebra and shows that it is the only invariant bilinear form on a simple Lie algebra. After a detour on properties of representations in chapter 5, wherein he constructs some useful relations for adjoint representations, the author uses these to again study the structure of simple Lie algebras in chapters 6 and 7. This involves the notion of positive and negative roots, and simple roots, and from the latter the author constructs the 'Cartan matrix', which summarizes all of the properties of the simple Lie algebra to which it corresponds. The author shows how the contents of the Cartan matrix can be summarized in terms of 'Dynkin diagrams'. These considerations allow an explicit characterization of the 'classical' Lie algebras: SU(n), SO(n), and Sp(2n) in chapter 8. The Dynkin diagrams of these Lie algebras are constructed. Then in chapter 9, the author considers the 'exceptional' Lie algebras, which are the last of the simple Lie algebras (5 in all). Their Dynkin diagrams are also constructed explicitly. The author returns to representation theory in chapter 10, wherein he introduces the concept of a 'weight'. These come in sequences with successive weights differing by the roots of the Lie algebra. A finite dimensional irreducible representation has a highest weight, and each greatest weight is specified by a set of non-negative integers called 'Dynkin coefficients'. He then shows how to classify representations as 'fundamental' or 'basic', the later being ones where the Dynkin coefficients are all zero except for one entry. In complete analogy with the theory of angular momenta in quantum mechanics, the author illustrates the role of Casimir operators in chapter 11. Freudenthal's recursion formula, which gives the dimension of the weight space, is used to derive Weyl's formula for the dimension of an irreducible representation in chapter 13. The reader can see clearly the power of the 'Weyl group' in exploiting the symmetries of representations.
A nice little summary of the theory |
10. Infinite-Dimensional Lie Algebras by Victor G. Kac | |
Paperback: 424
Pages
(1994-08-26)
list price: US$53.00 -- used & new: US$42.98 (price subject to change: see help) Asin: 0521466938 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
11. Lectures on Lie Groups and Lie Algebras (London Mathematical Society Student Texts) by Roger W. Carter, Ian G. MacDonald, Graeme B. Segal | |
Paperback: 200
Pages
(1995-09-29)
list price: US$47.00 -- used & new: US$39.34 (price subject to change: see help) Asin: 0521499224 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A very recommanded book on the subject |
12. Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras (Encyclopaedia of Mathematical Sciences) | |
Paperback: 248
Pages
(2010-11-02)
list price: US$149.00 -- used & new: US$134.10 (price subject to change: see help) Asin: 3642081207 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description A comprehensive and modern account of the structure and classification of Lie groups and finite-dimensional Lie algebras, by internationally known specialists in the field. This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics. |
13. Abstract Lie Algebras (Dover Books on Mathematics) by David J Winter | |
Paperback: 160
Pages
(2008-01-11)
list price: US$11.95 -- used & new: US$4.01 (price subject to change: see help) Asin: 048646282X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. It also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Contents include introductory material on prerequisites for modules and basic material on nonassociative algebras. 1972 edition. |
14. Lie Groups, Lie Algebras, Cohomology and some Applications in Physics (Cambridge Monographs on Mathematical Physics) by Josi A. de Azcárraga, Josi M. Izquierdo | |
Paperback: 455
Pages
(1998-09-13)
list price: US$90.00 -- used & new: US$79.54 (price subject to change: see help) Asin: 0521597005 Canada | United Kingdom | Germany | France | Japan | |
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15. Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics) by Jean-Pierre Serre | |
Paperback: 168
Pages
(1992-03-11)
list price: US$44.95 -- used & new: US$28.99 (price subject to change: see help) Asin: 3540550089 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Nice and complete, but very Bourbaki-looking. Thecontents of the book are: Lie algebras, filtered groups and lie algebras,universal algebra of a Lie algebra, free Lie algebras, nilpotent andsolvable Lie algebras, semisimple Lie algebras, representations of sl_n,complete fields, analytic functions, analytic manifolds, analytic groups,Lie theory. Includes excercises. Useful for graduate students and workingmathematicians, along with a "lighter" reference. Please checkmy other reviews (just click on my name above). ... Read more |
16. Lie Algebras In Particle Physics: from Isospin To Unified Theories (Frontiers in Physics) (Volume 0) by Howard Georgi | |
Paperback: 344
Pages
(1999-10-22)
list price: US$67.00 -- used & new: US$62.06 (price subject to change: see help) Asin: 0738202339 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5)theory. This extensively revised and updated edition of his classictext makes the theory of Lie groups accessible to graduate students,while offering a perspective on the way in which knowledge of suchgroups can provide an insight into the development of unified theoriesof strong, weak, and electromagnetic interactions. Customer Reviews (13)
i'll probably try to read it again, someday.
Covers the material very well
Simple and easy to read
Group Theory Supplement
classical |
17. An Introduction to Lie Groups and Lie Algebras (Cambridge Studies in Advanced Mathematics) by Alexander Kirillov Jr | |
Hardcover: 240
Pages
(2008-09-01)
list price: US$74.00 -- used & new: US$59.20 (price subject to change: see help) Asin: 0521889693 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
very, very good
An absolute must for beginners. |
18. Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory (Cambridge Monographs on Mathematical Physics) by Jürgen A. Fuchs | |
Paperback: 448
Pages
(1995-05-26)
list price: US$75.00 -- used & new: US$65.00 (price subject to change: see help) Asin: 052148412X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Affine Lie Algebras and Quantum Groups: An Introduction |
19. Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel, Rupert W. T. Yu | |
Paperback: 653
Pages
(2010-11-30)
list price: US$115.00 -- used & new: US$115.00 (price subject to change: see help) Asin: 3642063330 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters. |
20. Dictionary on Lie Algebras and Superalgebras by Luc Frappat, Antonino Sciarrino, Paul Sorba | |
Hardcover: 410
Pages
(2000-06-28)
list price: US$91.95 -- used & new: US$173.40 (price subject to change: see help) Asin: 0122653408 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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