Lie Algebras with Triangular Decompositions / Edition 1

by Robert V. Moody, Arturo Pianzola

Overview

Imparts a self-contained development of the algebraic theory of Kac-Moody algebras, their representations and close relatives—the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac-Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite-dimensional theory, Weyl groups and conjugacy theorems.

Product Details

ISBN-13:	9780471633044
Publisher:	Wiley
Publication date:	04/17/1995
Series:	Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts , #10
Pages:	712
Product dimensions:	6.46(w) x 9.53(h) x 1.38(d)

About the Author

Robert Vaughan Moody, OC FRSC is a Canadian mathematician. He is the co-discover of Kac-Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system. Arturo Pianzola is the author of Lie Algebras with Triangular Decompositions, published by Wiley.

Table of Contents

Lie Algebras.

Lie Algebras Admitting Triangular Decompositions.

Lattices and Root Systems.

Contragredient Lie Algebras.

The Weyl Group and Its Geometry.

Category O for Kac-Moody Algebras.

Conjugacy Theorems.

Appendix.

Bibliography.

Index.

Editorial Reviews

A text that presents a self-contained development of the algebraic theory of the Kac-Moody algebras, their representations, and their close relatives, the Virasoro and Heisenberg algebras. It concentrates on developing the theory of triangular decompositions and the part of the Kac-Moody theory not specific to the affine case. A secondary theme is the subject of lattices (discrete subgroups of Rn carrying an integral-valued symmetric bilinear form). Numerous exercises conclude each chapter. Assumes a reasonable background in linear algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews