An Introduction to Lie Groups and Lie Algebras

AvAlexander Kirillov, Jr Jr

Häftad, Engelska, 2017

Del 113 i serien Cambridge Studies in Advanced Mathematics

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Beskrivning

With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York, Stony Brook, the book includes numerous exercises and worked examples, and is ideal for graduate courses on Lie groups and Lie algebras.

Produktinformation

Utgivningsdatum:2017-04-06
Mått:152 x 229 x 13 mm
Vikt:322 g
Format:Häftad
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:236
Förlag:Cambridge University Press
ISBN:9781316614105

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Alexander Kirillov, Jr, is an Associate Professor in the Mathematics Department, State University of New York, Stony Brook. His research interests are representation theory, Lie algebras, quantum groups, affine Lie algebras and conformal field theory.

Recensioner i media

'… the exposition is very clear and logical. It has the advantage of giving the basic facts about Lie algebra theory with enough arguments but skipping the tedious technical details of proofs. Another excellent feature of the book is that many of the basic notions, properties and results are illustrated by a great number of exercises and examples. In my opinion this book is a nice addition to the landmarks in the field … I strongly recommend it to anyone wishing to enter into the beautiful and exciting field of Lie algebras and their applications.' Journal of Geometry and Symmetry in Physics

Innehållsförteckning

Preface; 1. Introduction; 2. Lie groups: basic definitions; 3. Lie groups and Lie algebras; 4. Representations of Lie groups and Lie algebras; 5. Structure theory of Lie algebras; 6. Complex semisimple Lie algebras; 7. Root systems; 8. Representations of semisimple Lie Algebras; Overview of the literature; A. Root systems and simple Lie algebras; B. Sample syllabus; List of notation; Index; Bibliography.