Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Nonfiction, Science & Nature, Mathematics, Group Theory, Topology
Cover of the book Introduction to Finite and Infinite Dimensional Lie (Super)algebras by Neelacanta Sthanumoorthy, Elsevier Science
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Author: Neelacanta Sthanumoorthy ISBN: 9780128046838
Publisher: Elsevier Science Publication: April 26, 2016
Imprint: Academic Press Language: English
Author: Neelacanta Sthanumoorthy
ISBN: 9780128046838
Publisher: Elsevier Science
Publication: April 26, 2016
Imprint: Academic Press
Language: English

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
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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.

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