An introduction to Lie groups and Lie algebras / / Alexander Kirillov, Jr [[electronic resource]]

• Record Nr.: UNINA9910453177203321
• Autore: Kirillov Alexander A. <1967->
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2008
• ISBN: 1-107-18764-8; 1-316-61410-7; 1-281-77569-X; 9786611775698; 0-511-42370-5; 0-511-42253-9; 0-511-42418-3; 0-511-42187-7; 0-511-75515-5; 0-511-42319-5
• Descrizione fisica: 1 online resource (ix, 222 pages) : digital, PDF file(s)
• Collana: Cambridge studies in advanced mathematics ; ; 113
• Disciplina: 512/.482
• Soggetti: Lie groups; 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 (p. 216-219) and index.
• Nota di contenuto: Introduction -- Lie groups: basic definitions -- Lie groups and Lie algebras -- Representation of Lie groups and Lie algebras -- Structure theory of Lie algebras -- Complex semisimple Lie algebras -- Root systems -- Representation of semisimple Lie algebras -- Overview of the literature -- Appendix A: Root systems and simple Lie algebras -- Appendix B: Sample syllabus -- List of notation.
• Sommario/riassunto: 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 at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.