eBook ISBN:  9780821876985 
Product Code:  CONM/110.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876985 
Product Code:  CONM/110.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 110; 1990; 313 ppMSC: Primary 17
The 1984 classification of the finitedimensional 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 198788. Work done during the Special Year and afterward put researchers much closer toward a solution of the longstanding problem of determining the finitedimensional 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 KacMoody 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

Articles

B. N. Allison — Isotropic simple Lie algebras of type $D_4$ [ MR 1079097 ]

S. Berman — On involutory subalgebras of KacMoody Lie algebras [ MR 1079098 ]

Gordon Brown — Structure of certain simple Lie algebras of characteristic three [ MR 1079099 ]

Robert W. Deckhart — Calculus of some functions on the root lattice [ MR 1079100 ]

J. Dorfmeister, E. Neher and J. Szmigielski — Banach manifolds and their automorphisms associated with groups of type $C_\infty $ and $D_\infty $ [ MR 1079101 ]

Alex J. Feingold, John F. X. Ries and Igor B. Frenkel — The exceptional affine algebra $E^{(1)}_8,$ triality and chiral algebras [ MR 1079102 ]

Thomas B. Gregory — A characterization of the general Lie algebras of Cartan type $W(n:{\bf m})$ [ MR 1079103 ]

W. G. McKay, R. V. Moody, J. Patera and A. Pianzola — The 785 conjugacy classes of rational elements of finite order in $E_8$ [ MR 1079104 ]

Walter Michaelis — The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra [ MR 1079105 ]

Kailash C. Misra — On irreducible highest weight representations of some affine Lie algebras [ MR 1079106 ]

Brian J. Parshall — Hyperalgebras, highest weight categories and finitedimensional algebras [ MR 1079107 ]

John G. Ryan — Extensions of representations of semisimple Lie algebras [ MR 1079108 ]

John Schue — Enveloping algebras and division rings for Lie $p$algebras [ MR 1079109 ]

P. E. Singer — Serre relations [ MR 1079110 ]

Louis Solomon — The number of irreducible representations of a finite Coxeter group [ MR 1079111 ]

Helmut Strade — The role of $p$envelopes in the theory of modular Lie algebras [ MR 1079112 ]

Vicente R. Varea — On modular subalgebras in Lie algebras of prime characteristic [ MR 1079113 ]

Dave Witte — Cocompact subgroups of semisimple Lie groups [ MR 1079114 ]


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The 1984 classification of the finitedimensional 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 198788. Work done during the Special Year and afterward put researchers much closer toward a solution of the longstanding problem of determining the finitedimensional 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 KacMoody 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.

Articles

B. N. Allison — Isotropic simple Lie algebras of type $D_4$ [ MR 1079097 ]

S. Berman — On involutory subalgebras of KacMoody Lie algebras [ MR 1079098 ]

Gordon Brown — Structure of certain simple Lie algebras of characteristic three [ MR 1079099 ]

Robert W. Deckhart — Calculus of some functions on the root lattice [ MR 1079100 ]

J. Dorfmeister, E. Neher and J. Szmigielski — Banach manifolds and their automorphisms associated with groups of type $C_\infty $ and $D_\infty $ [ MR 1079101 ]

Alex J. Feingold, John F. X. Ries and Igor B. Frenkel — The exceptional affine algebra $E^{(1)}_8,$ triality and chiral algebras [ MR 1079102 ]

Thomas B. Gregory — A characterization of the general Lie algebras of Cartan type $W(n:{\bf m})$ [ MR 1079103 ]

W. G. McKay, R. V. Moody, J. Patera and A. Pianzola — The 785 conjugacy classes of rational elements of finite order in $E_8$ [ MR 1079104 ]

Walter Michaelis — The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra [ MR 1079105 ]

Kailash C. Misra — On irreducible highest weight representations of some affine Lie algebras [ MR 1079106 ]

Brian J. Parshall — Hyperalgebras, highest weight categories and finitedimensional algebras [ MR 1079107 ]

John G. Ryan — Extensions of representations of semisimple Lie algebras [ MR 1079108 ]

John Schue — Enveloping algebras and division rings for Lie $p$algebras [ MR 1079109 ]

P. E. Singer — Serre relations [ MR 1079110 ]

Louis Solomon — The number of irreducible representations of a finite Coxeter group [ MR 1079111 ]

Helmut Strade — The role of $p$envelopes in the theory of modular Lie algebras [ MR 1079112 ]

Vicente R. Varea — On modular subalgebras in Lie algebras of prime characteristic [ MR 1079113 ]

Dave Witte — Cocompact subgroups of semisimple Lie groups [ MR 1079114 ]