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Lie Algebras and Related Topics
Edited by: Georgia Benkart and J. Marshall Osborn
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Contemporary Mathematics
1990; 313 pp; softcover
Volume: 110
ISBN-10: 0-8218-5119-5
ISBN-13: 978-0-8218-5119-7
List Price: US$56
Member Price: US$44.80
Order Code: CONM/110
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The 1984 classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic \(p>7\) provided the impetus for a Special Year of Lie Algebras, held at the University of Wisconsin, Madison, during 1987-88. Work done during the Special Year and afterward put researchers much closer toward a solution of the long-standing problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic \(p>7\).

This volume contains the proceedings of a conference on Lie algebras and related topics, held in May 1988 to mark the end of the Special Year. The conference featured lectures on Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras. Many facets of recent research on Lie theory are reflected in the papers presented here, testifying to the richness and diversity of this topic.

Table of Contents

  • B. N. Allison -- Isotropic simple Lie algebras of type \(D_4\)
  • S. Berman -- On involutory subalgebras of Kac-Moody Lie algebras
  • G. Brown -- Structure of certain simple Lie algebras of characteristic three
  • R. W. Deckhart -- Calculus of some functions on the root lattice
  • J. Dorfmeister, E. Neher, and J. Szmigielski -- Banach manifolds and their automorphisms associated with groups of type \(C_\infty\) and \(D_\infty\)
  • A. J. Feingold, I. B. Frenkel, and J. F. X. Ries -- The exceptional affine algebra \(E_8^(1)\), triality and Chiral algebras
  • T. B. Gregory -- A characterization of the general Lie algebras of Cartan type \(W(n:\underline\underline m)\)
  • W. G. McKay, R. V. Moody, J. Patera, and A. Pianzola -- The 785 conjugacy classes of rational elements of finite order in \(E_8\)
  • E. Michaelis -- The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra
  • K. C. Misra -- On irreducible highest weight representations of some affine Lie algebras
  • B. J. Parshall -- Hyperalgebras, highest weight categories and finite dimensional algebras
  • J. G. Ryan -- Extensions of representations of semisimple Lie algebras
  • J. Schue -- Enveloping algebras and division rings for Lie \(p\)-algebras
  • P. E. Singer -- Serre relations
  • L. Solomon -- The number of irreducible representations of a finite coxeter group
  • H. Strade -- The role of \(p\)-envelopes in the theory of modular Lie algebras
  • V. R. Varea -- On modular subalgebras in Lie algebras of prime characteristic
  • D. Witte -- Cocompact subgroups of semisimple Lie groups
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