1.

Record Nr.

UNINA9910819710803321

Autore

Henderson Anthony <1976->

Titolo

Representations of Lie algebras : an introduction through gln / / Anthony Henderson, School of Mathematics and Statistics, University of Sydney [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2012

ISBN

1-139-56498-6

1-316-09056-6

1-139-23612-1

1-283-57524-8

1-139-55145-0

9786613887696

1-139-55641-X

1-139-55271-6

1-139-55020-9

1-139-55516-2

Descrizione fisica

1 online resource (ix, 156 pages) : digital, PDF file(s)

Collana

Australian Mathematical Society lecture series ; ; 22

Classificazione

MAT002000

Disciplina

512/.482

Soggetti

Representations of Lie algebras

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Machine generated contents note: 1. Motivation: representations of Lie groups; 2. Definition of a Lie algebra; 3. Basic structure of a Lie algebra; 4. Modules over a Lie algebra; 5. The theory of SL2-modules; 6. General theory of modules; 7. Integral GLn-modules; 8. Guide to further reading; Appendix: solutions to the exercises; Bibliography; Index.

Sommario/riassunto

This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest



generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.