Algebra 4 : lie algebras, Chevalley groups, and their representations / Ramji Lal.

Format:

Book

Author/Creator:

Lal, Ramji, author.

Series:

Infosys Science Foundation series.

Infosys Science Foundation Series

Language:

English

Subjects (All):

Algebra.

Algebra--Textbooks.

Physical Description:

1 online resource (332 pages).

Other Title:

Algebra four

Place of Publication:

Singapore : Springer, [2021]

Summary:

This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and representation theory in detail. It covers topics such as semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups and representation theory of Chevalley groups. Numerous motivating illustrations have been presented along with exercises, enabling readers to acquire a good understanding of topics which they can then use to find the exact or most realistic solutions to their problems.

Contents:

Intro

Preface

Contents

About the Author

Notations

1 Lie Algebras

1.1 Definitions and Examples

1.2 Universal Enveloping Algebras: PBW Theorem

1.3 Solvable and Nilpotent Lie Algebras

1.4 Semi-Simple Lie Algebras

1.5 Extensions of Lie Algebras and Co-homology

2 Semi-Simple Lie Algebras and Root Systems

2.1 Root Space Decomposition

2.2 Root Systems

2.3 Dynkin Diagram and the Classification of Root Systems

2.4 Conjugacy Theorem, Existence and Uniqueness Theorems

3 Representation Theory of Lie Algebras

3.1 Theorems of Ado and Iwasawa

3.2 Cyclic Modules and Weights

3.3 Characters and Harish-Chandra's Theorem

3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg

4 Chevalley Groups

4.1 Classical Linear Groups

4.2 Chevalley Basis

4.3 Chevalley Groups

4.4 Twisted Groups

5 Representation Theory of Chevalley Groups

5.1 Language of Representation Theory

5.2 Representations of Sn, and of GL(2.q)

5.3 Steinberg Characters

5.4 Principal and Discrete Series Representations

5.5 Deligne-Lusztig Generalized Characters

Appendix Bibliography

Index.

Notes:

Description based on print version record.

ISBN:

981-16-0475-4

OCLC:

1244622358