1.

Record Nr.

UNISA996466559403316

Autore

Lal Ramji

Titolo

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

Pubbl/distr/stampa

Singapore : , : Springer, , [2021]

©2021

ISBN

981-16-0475-4

Descrizione fisica

1 online resource (332 pages)

Collana

Infosys Science Foundation Series

Disciplina

512.9

Soggetti

Algebra

Àlgebra

Llibres de text

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.