41. OSU Lie Algebra Conference, 1971 lie algebra Conference, 1971. Photograph taken at a conference onlie algebras in 1971, on the front steps of the Ohio Union. In http://www.math.ohio-state.edu/history/album/Picture3.html

Photograph taken at a conference on Lie algebras in 1971, on the front steps of the Ohio Union. In the front row on the extreme left is Arnold Ross, directly behind Bob Brown. Two places to the right of Ross is Hans Zassenhaus. Second from the right in the front row is Nathan Jacobson and two places to the left of him is A. Adrian Albert. In the last row, first from the left is Harry Allen, second from the right Joe Ferrar, with George Seligman to his right. Conference organizers were Allen, Brown, and Ferrar. (Photo donated by Mrs. Zassenhaus.) Click on the picture for an oversized closeup.

42. LIE ALGEBRA OF THE lie algebra OF THE i q /i POINCARÉ GROUP AND i q /i -HEISENBERGCOMMUTATION RELATIONS. http://www.worldscinet.com/ijmpb/13/1324_25/S021797929900271X.html

q q -HEISENBERG COMMUTATION RELATIONS What's New New Journals Browse Journals Search ... doi:10.1142/S021797929900271X LIE ALGEBRA OF THE q q -HEISENBERG COMMUTATION RELATIONS PAOLO ASCHIERI Theoretical Physics Group, Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA We discuss quantum orthogonal groups and their real forms. We review the construction of inhomogeneous orthogonal q -groups and their q -Lie algebras. The geometry of the q q -deformed Heisenberg algebra of hermitian q -Minkowski coordinates x a and momenta p a Footnotes: E-mail: aschieri@lbl.gov This work is supported by CNR grant bando 203.01.66. It is in part supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and by the National Science Foundation under grant PHY-95-14797. PDF SOURCE (406 k)

43. OCTONIONS AND SUPER-LIE ALGEBRA OCTONIONS AND SUPERlie algebra. KHALED ABDEL operators. As an examplewe construct explicitly some Lie and super-lie algebra. Then http://www.worldscinet.com/ijmpa/13/1302/halek.html

International Journal of Modern Physics A, Vol. 13, No. 2 (1998) 223-231 OCTONIONS AND SUPER-LIE ALGEBRA KHALED ABDEL-KHALEK E-mail We discuss how to represent the nonassociative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and super-Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace formulation of the minimal supersymmetric Yang–Mills models. PDF SOURCE Back to Contents of Vol. 13, No. 2

44. The First Integrals And Their Lie Algebra Of The Most General Autonomous Hamilto The first integrals and their lie algebra of the most general autonomous Hamiltonianof the form H = T + V possessing a LaplaceRunge-Lenz vector. http://anziamj.austms.org.au/V34/part4/Gorringe.html

J Austral Math Soc Ser B The first integrals and their Lie algebra of the most general autonomous Hamiltonian of the form H = T + V possessing a Laplace-Runge-Lenz vector V. M. Gorringe and P. G. L. Leach (Received 9 April 1990; revised 6 May 1992) Abstract In two dimensions it is found that the most general autonomous Hamiltonian possessing a Laplace-Runge-Lenz vector is H r r cos(( )/2). The Poisson bracket of the two components of this vector leads to a third first-integral, cubic in the momenta. The Lie algebra of the three integrals under the operation of the Poisson bracket closes, and is shown to be so (3) for negative energy and so (2, 1) for positive energy. In the case of zero energy, the algebra is W (3,1). The result does not have a three-dimensional analogue, apart from the usual Kepler problem. Browse the article Read the article in your browser. (Print at 75% on A4 paper). Authors V. M. Gorringe P. G. L. Leach Centre for Nonlinear Studies and Department of Computational and Applied Mathematics, University of the Witwatersrand, P.O. WITS, 2050 South Africa. Editor JAMSB(E) WWW Administrator Last Modified: Tue Aug 8 12:54:07 2000

45. The Rational Adjoint Orbits Of A Lie Algebra Of Type G2 (Jackson) The rational adjoint orbits of a lie algebra of type G2. Author. DavidGA Jackson. Status. Research Report 9819 Date 30 July 1998. Abstract. http://www.maths.usyd.edu.au:8000/res/Algebra/Jac/1998-19.html

The rational adjoint orbits of a Lie algebra of type G2 Author David G. A. Jackson Status Research Report 98-19 Date: 30 July 1998 Abstract In 1968, Chang classified the rational conjugacy classes of a Chevalley group of type G2. In this paper we study the analogous problem of classifying the rational adjoint orbits of a Lie algebra of type G2. Key phrases Chevalley group. adjoint orbit. reductive group. regular element. AMS Subject Classification (1991) Primary: 20G40 Secondary: 17B45 Content The paper is available in the following forms: TeX dvi format: 1998-19.dvi.gz (67kB) or 1998-19.dvi PostScript: 1998-19.ps.gz (140kB) or 1998-19.ps To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it. Sydney Mathematics and Statistics

46. Rational Regular Nilpotent Elements Of A Reductive Lie Algebra (Jackson) Rational regular nilpotent elements of a reductive lie algebra. Author. David GAJackson. Status. lie algebra. reductive group. AMS Subject Classification (1991). http://www.maths.usyd.edu.au:8000/res/Algebra/Jac/1998-20.html

Rational regular nilpotent elements of a reductive Lie algebra Author David G. A. Jackson Status Research Report 98-20 Date: 30 July 1998 Abstract Key phrases regular element. nilpotent element. Lie algebra. reductive group. AMS Subject Classification (1991) Primary: 20G40 Secondary: 17B45 Content The paper is available in the following forms: TeX dvi format: 1998-20.dvi.gz (19kB) or 1998-20.dvi PostScript: 1998-20.ps.gz (49kB) or 1998-20.ps To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it. Sydney Mathematics and Statistics

47. Seminarium Oneindig Dimensionale Lie Algebra's Seminarium oneindig dimensionale lie algebra's. Terug naar de home page.Seminarium Dinsdag 900 1045, zaal 611B. Eerste bijeenkomst http://www.math.uu.nl/people/ban/liesem2000/liesem2000.html

Seminarium oneindig dimensionale Lie algebra's Terug naar de home page. Seminarium: Dinsdag 9:00 - 10:45, zaal 611B. Eerste bijeenkomst: dinsdag 5 september Nadere informatie: hier aanklikken Extra materiaal: Aantekeningen over tensoren Docenten 2000: E.P. van den Ban , kamer 609, Wiskundegebouw, Budapestlaan 6. J. van de Leur , kamer 413, Wiskundegebouw, Budapestlaan 6. Email: 17 januari 2000

48. When Is A Lie Algebra Not A Lie Algebra? When is a lie algebra not a lie algebra? Abstract. We look at weight systems on Feynmandiagrams. A metric lie algebra gives one example of a weight system. http://www.math.sunysb.edu/~sawon/lie_alg_obj.shtml

When is a Lie algebra not a Lie algebra? Abstract We look at weight systems on Feynman diagrams. A metric Lie algebra gives one example of a weight system. More generally, a `Casimir Lie algebra object' in an arbitrary linear tensor category also gives a weight system. We look at an example in the category of graded vector spaces coming from the cohomology of a holomorphic symplectic manifold. We then look at how various results for Lie algebras may be rephrased as results for these `Lie algebra objects'. Appears in the Informal Proceedings of the IXth Oporto Meeting on Geometry, Topology and Physics (available electronically). Back to the main page This page last modified by Justin Sawon Tuesday, 10-Sep-2002 11:29:27 EDT Email corrections and comments to sawon@math.sunysb.edu

49. [math/0002223] Multipartitions, Generalized Durfee Squares And Affine Lie Algebr 0914 GMT (12kb) Multipartitions, Generalized Durfee Squares andAffine lie algebra Characters. Authors Peter Bouwknegt Comments http://arxiv.org/abs/math.co/0002223

Mathematics, abstract math.CO/0002223 Multipartitions, Generalized Durfee Squares and Affine Lie Algebra Characters Authors: Peter Bouwknegt Comments: LaTeX2e, 14 pages Report-no: ADP-00-01/M87 Subj-class: Combinatorics; Quantum Algebra MSC-class: We give some higher dimensional analogues of the Durfee square formula and point out their relation to dissections of multipartitions. We apply the results to write certain affine Lie algebra characters in terms of Universal Chiral Partition Functions. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv math find abs

50. [hep-th/9302138] The Lie Algebra Of Sl(2)-valued Automorphic Functions On A Toru 140758 0500 (EST) (9kb) The lie algebra of sl(2)-valued automorphicfunctions on a torus. Author DB Uglov Comments 13 pages http://arxiv.org/abs/hep-th/9302138

High Energy Physics - Theory, abstract hep-th/9302138 From: denis@insti.physics.sunysb.edu (Denis Uglov) Date: 26 Feb 1993 14:07:58 -0500 (EST) (9kb) The Lie algebra of sl(2)-valued automorphic functions on a torus Author: D. B. Uglov Comments: 13 pages Subj-class: High Energy Physics - Theory; Quantum Algebra Journal-ref: Lett.Math.Phys. 31 (1994) 65-76 It is shown that the Lie algebra of the automorphic, meromorphic sl(2, C) -valued functions on a torus is a geometric realization of a certain infinite-dimensional finitely generated Lie algebra. In the trigonometric limit, when the modular parameter of the torus goes to zero, the former Lie algebra goes over into the sl(2,C) -valued loop algebra, while the latter one - into the Lie algebra (sl(2)^)'/(centre) . Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Links to: arXiv hep-th find abs

51. Liegroups And Lie-algebra -- Index Liegroups and Liealgebra. A general introduction to the mathematical foundationsof Lie group and lie algebra theory, with special attention to applications. http://aivwww.rug.ac.be/Studentenadministratie/Studiegids/2002/EN/FACULTY/C_WE/C

Liegroups and Lie-algebra Reference Lectured in Optional Course List Second Cycle Mathematics Theory (A) Exercises (B) Training and projects (C) Studytime (D) Studypoints (E) Language of instruction Dutch Lecturer Frans Cantrijn Semester second Department Co-lecturers Key Words Objectives A general introduction to the mathematical foundations of Lie group and Lie algebra theory, with special attention to applications. The treatment is mainly restricted to real, finite dimensional Lie groups and algebras. Contents Lie algebras (definition and general properties); topological groups; differentiable manifolds; Lie groups (definition and general properties); the Lie algebra of a Lie group; Lie subgroups and Lie subalgebras; homomorphisms of Lie groups; locally isomorphic Lie groups; exponential map; adjoint representation of Lie groups and Lie algebras; transformation groups and symmetries of dynamical systems; examples of linear Lie groups (orthogonal group, unitary group, Lorentz group, ...); structure of Lie algebras. Course Material a syllabus is available References V.S. Varadarajan :

52. Infinite-Dimensional Lie Algebra; Author: Wakimoto, Minoru; Hardback; Book InfiniteDimensional lie algebra Author Wakimoto, Minoru - Hardback;Book, ENGLISH BOOKS DEPARTMENT, Join the NetStore Cooperative, http://www.opengroup.com/mabooks/981/9810241283.shtml

English Books German Books Spanish Books Sheet Music ... NEW RELEASES Infinite-Dimensional Lie Algebra Author: Wakimoto, Minoru Hardback; Book 456 pages Published: October 2001 World Scientific Publishing Co Pte Ltd ISBN: 9810241283 This item non-returnable. Order may not be canceled. PRODUCT CODE: 9810241283 USA/Canada: US$ 158.90 Australia/NZ: A$ 152.95 Other Countries: US$ 179.30 convert to your currency Delivery costs included if your total order exceeds US$50. We do not charge your credit card until we ship your order. Government and corporate Purchase Orders accepted without prior account application. PLACE AN ORDER To prepare to buy this item click "add to cart" above. You can change or abandon your shopping cart at any time before checkout. CHECK ORDER STATUS Check on order progress and dispatch. CHANGE OR CANCEL YOUR ORDER Please E-mail us within one hour The NetStoreUSA website is operated by Open Communications, Inc an Arizona corporation, which has successfully served the Internet community since 1994. Site Design by GillespieFox ( www.gillespiefox.com

53. Infinite-Dimensional Lie Algebra; Author: Wakimoto, Minoru; Paperback InfiniteDimensional lie algebra Author Wakimoto, Minoru - Paperback,ENGLISH BOOKS DEPARTMENT, Join the NetStore Cooperative, http://www.opengroup.com/mabooks/981/9810241291.shtml

English Books German Books Spanish Books Sheet Music ... NEW RELEASES Infinite-Dimensional Lie Algebra Author: Wakimoto, Minoru Paperback 456 pages Published: October 2001 World Scientific Publishing Co Pte Ltd ISBN: 9810241291 PRODUCT CODE: 9810241291 USA/Canada: US$ 55.90 Australia/NZ: A$ 97.95 Other Countries: US$ 89.80 convert to your currency Delivery costs included if your total order exceeds US$50. We do not charge your credit card until we ship your order. Government and corporate Purchase Orders accepted without prior account application. PLACE AN ORDER To prepare to buy this item click "add to cart" above. You can change or abandon your shopping cart at any time before checkout. CHECK ORDER STATUS Check on order progress and dispatch. CHANGE OR CANCEL YOUR ORDER Please E-mail us within one hour The NetStoreUSA website is operated by Open Communications, Inc an Arizona corporation, which has successfully served the Internet community since 1994. Site Design by GillespieFox ( www.gillespiefox.com ®Open Communications is a Registered Trade Mark. This material may be freely distributed ONLY with full reference to Open Communications Inc including fax, phone, e-mail, and world-wide web details.

54. MA 792M: Lie Algebra Special Topics - Presentation Notes MA 792M lie algebra Special Topics Presentation Notes. I presented a constructionof the exceptional simple lie algebra G2. Here are my notes. Source http://www4.ncsu.edu:8030/~wjcook/ma792/

MA 792M: Lie Algebra Special Topics - Presentation Notes William Jeffrey Cook, Department of Mathematics, North Carolina State University I presented a construction of the exceptional simple Lie algebra G2. Here are my notes. Source... Paper (tex) Paper (lyx - for LyX Editor) Paper (pdf - for Adobe Acrobat) B3's Root System ... G2's Root System with Root Space Decomposition Some of my old tests and projects require a "pdf" viewer. If you don't have a "pdf" viewer goto Adobe's Homepage and download "Adobe Acrobat"

55. Lie Algebra lie algebra. BT linear algebra FT algebre de liePrevious Item Next Item Search Help. http://irc.nrc-cnrc.gc.ca/thesaurus/lie_algebra.html

lie algebra BT linear algebra FT algebre de lie [Previous Item] [Next Item] [Search] [Help]

56. [FPLSA] 1 The FPLSA Package At present GAP uses only the facility to compute a structure constants table ofa finitedimensional lie algebra over the rationals that is given by a finite http://www-gap.dcs.st-and.ac.uk/~gap/pkg/fplsa/htm/CHAP001.htm

Up Index 1 The FPLSA Package Sections Main Functions Auxiliary Variables of FPLSA Installing the FPLSA Package This chapter describes the FPLSA package, an interface to the fplsa program by V. Gerdt and V. Kornyak (version 4) for the computation with finitely presented Lie superalgebras. At present GAP uses only the facility to compute a structure constants table of a finite-dimensional Lie algebra over the rationals that is given by a finite presentation. As the package uses an external binary, it will only work on UNIX platforms. 1.1 Main Functions A finitely-presented Lie algebra is a quotient of a free Lie algebra by an ideal generated by a finite number of elements. In GAP a free Lie algebra can be created by the command FreeLieAlgebra ; we refer to the reference manual for more details. A finitely presented Lie algebra K can be constructed by K L rels , where L is a free Lie algebra and rels a list of elements of L that constitute the relations that hold in K . Given a finitle presented Lie algebra we want to calculate a basis and a multiplication table of it. The interface to the FPLSA package comes with two related functions for doing that.

57. Dynamical Lie Algebra And Conditional Operators For Many Fermion Green Functions Center. O38.90 Dynamical lie algebra and Conditional Operators ForMany Fermion Green Functions. Jay Mancini (Fordham University). http://www.aps.org/BAPSMAR98/abs/S3150090.html

Previous abstract Graphical version Next abstract Session O38 - General Poster Session III and DHPP Poster Session I. POSTER session, Wednesday morning, March 18 Exhibit Hall, Los Angeles Convention Center Dynamical Lie Algebra and Conditional Operators For Many Fermion Green Functions Jay Mancini (Fordham University) A method is introduced to calculate thermodynamic Green functions. A powerful theorem by Masson is the motivation for expressing the Fourier-time transform of the Green function as a super space matrix element of the resolvent of the Liouville operator. The eigenvalues of the Liouville operator are then expressed in a form first suggested by Judd for atomic systems and which are shown to be members of Lie group. Part O of program listing

58. Dynamical Lie Algebra And Conditional Operators For Many Fermion Green Functions Previous abstract Graphical version Text version Next abstractSession O38 General Poster Session III and DHPP Poster Session http://www.aps.org/BAPSMAR98/abs/G3150090.html

Previous abstract Text version Next abstract Session O38 - General Poster Session III and DHPP Poster Session I. POSTER session, Wednesday morning, March 18 Exhibit Hall, Los Angeles Convention Center Dynamical Lie Algebra and Conditional Operators For Many Fermion Green Functions Jay Mancini (Fordham University) Part O of program listing

59. We Compute The Rational Homotopy Lie Algebra And Rational Cohomology And The $G$sequence of a map $f X \rightarrow Y$ is a boundary sequencerelating the Gottlieb. group $G_*(X)$ of the space $X$ to the http://www.sju.edu/~smith/Abstracts/paper9.htm

simply connected CW complexes with $X$ finite, we identify the rationalization of the $G$-sequence in higher degrees as a sequence of derivation spaces of differential graded rational algebras. Using this result, we give new examples of nonexact $G$-sequences, uncover a relationship between the homology of the rational $G$-sequence and negative derivations of rational cohomology and analyze the splitting of the rational as a measure of the triviality of a fibration

60. We Compute The Rational Homotopy Lie Algebra And Rational Cohomology And We identify the rationalization. of $G_{*}(Y, X;f),$ Gottlieb's generalizedevaluation group of a map. $f X \to Y.$ Extending a http://www.sju.edu/~smith/Abstracts/paper10.htm

We identify the rationalization adjoint representation induced by $f$ on Quillen models.

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