Introduction to Finite and Infinite Dimensional Lie (Super)Algebras

ISBN-13: 9780128046753 / Angielski / Twarda / 2016 / 512 str.

Sthanumoorthy Neelacanta

Opis

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

• Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory
• Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities
• Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras
• Focuses on Kac-Moody algebras

Recenzje

"...it's a dense book, not meant for neophytes, notwithstanding its many exercises. It is a very good book, I think, and remarkable for its sweep." --MAA Reviews

Spis treści

1. Finite dimensional Lie Algebras

2. Kac-Moody algebras

3. Generalized Kac-Moody algebras

4. Lie superalgebras

5. Borcherds Kac-Moody Lie superalgebras

6. Lie algebras of Lie groups, Kac-Moody groups, supergroups and some specialized topics in finite and infinite dimensional Lie algebras

O autorze

N. Sthanumoorthy has 45 years of teaching and research experience. Formerly Professor and Professor Emeritus, Dr Sthanumoorthy is presently the Principal Investigator of a Book-Writing Project funded by "Science and Engineering Research Board - Department of Science and Technology, Government of India” in RIASM, University of Madras, India. He has published several research papers on topics closely related to the title of the present book, guided many Ph.D. scholars and evaluated several Ph.D. theses. He was an editor of Kac-Moody Lie Algebras and Related topics, which published as volume 343 of 'Contemporary Mathematics (AMS)', and he is a reviewer for Mathematical Reviews. He delivered lectures in many institutions in the USA, Germany, Italy, China, and India. Many awards and honors were also conferred on the author.