Lie groups, lie algebras, and cohomology / by Anthony W. Knapp.

Format:

Book

Author/Creator:

Knapp, Anthony W., author.

Series:

Mathematical Notes ; 108

Language:

English

Subjects (All):

Lie groups.

Physical Description:

1 online resource (xii, 509 pages) : illustrations

Place of Publication:

Princeton, New Jersey : Princeton University Press, [1988]

Summary:

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

Contents:

Frontmatter

CONTENTS

PREFACE

CHAPTER I. LIE GROUPS AND LIE ALGEBRAS

CHAPTER II. REPRESENTATIONS AND TENSORS

CHAPTER III. REPRESENTATIONS OP COMPACT GROUPS

CHAPTER IV. COHOMOLOGY OF LIE ALGEBRAS

CHAPTER V. HOMOLOGICAL ALGEBRA

CHAPTER VI. APPLICATION TO LIE ALGEBRAS

CHAPTER VII. RELATIVE LIE ALGEBRA COHOMOLOGY

CHAPTER VIII. REPRESENTATIONS OF NONCOMPACT GROUPS

NOTES

REFERENCES

INDEX OF NOTATION

INDEX

Notes:

Description based on print version record.

ISBN:

9780691223803

0691223807

OCLC:

1312726686