Author: H. Omori
Publisher: Springer
ISBN: 3540372954
Category : Mathematics
Languages : en
Pages : 165

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Book Description

Author: Neelacanta Sthanumoorthy
Publisher: Academic Press
ISBN: 012804683X
Category : Mathematics
Languages : en
Pages : 514

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Book Description
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

Author: Minoru Wakimoto
Publisher: World Scientific
ISBN: 9814494003
Category : Mathematics
Languages : en
Pages : 456

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Book Description
The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.

Author: Hideki Omori
Publisher:
ISBN:
Category : Lie groups
Languages : en
Pages : 150

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Book Description

Author: H. Omori
Publisher:
ISBN: 9783662206553
Category :
Languages : en
Pages : 168

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Book Description

Author: Augustin Banyaga
Publisher: World Scientific
ISBN: 9814488143
Category : Science
Languages : en
Pages : 174

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Book Description
This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics.

Author: Hideki Omori
Publisher: American Mathematical Soc.
ISBN: 1470426358
Category :
Languages : en
Pages : 434

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Book Description
This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.

Author: V.V. Gorbatsevich
Publisher: Springer Science & Business Media
ISBN: 9783540612223
Category : Mathematics
Languages : en
Pages : 552

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Book Description
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Author:
Publisher: Academic Press
ISBN: 0080873596
Category : Mathematics
Languages : en
Pages : 477

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Book Description
Introduction to Compact Transformation Groups

Author: Alexander A. Kirillov
Publisher: Cambridge University Press
ISBN: 0521889693
Category : Mathematics
Languages : en
Pages : 237

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Book Description
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.