Classical Lie Algebras at Infinity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Classical Lie Algebras at Infinity write by Ivan Penkov. This book was released on 2022-01-05. Classical Lie Algebras at Infinity available in PDF, EPUB and Kindle. Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Stability in Modules for Classical Lie Algebras: A Constructive Approach
Stability in Modules for Classical Lie Algebras: A Constructive Approach - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stability in Modules for Classical Lie Algebras: A Constructive Approach write by Georgia Benkart. This book was released on 1990. Stability in Modules for Classical Lie Algebras: A Constructive Approach available in PDF, EPUB and Kindle. In this work we consider the problem of determining information about representations as the rank grows large, in fact, tends to infinity. Here we show that the set of dominant weights stabilizes as the rank goes to infinity and the multiplicities become polynomials in the rank. In addition, we give effective, easily computable algorithms for determining the set of dominant weights and illustrate how to calculate their multiplicity polynomials.
Infinite Dimensional Lie Algebras
Infinite Dimensional Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Infinite Dimensional Lie Algebras write by Victor G. Kac. This book was released on 2013-11-09. Infinite Dimensional Lie Algebras available in PDF, EPUB and Kindle.
Lectures on Infinite-dimensional Lie Algebra
Lectures on Infinite-dimensional Lie Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Infinite-dimensional Lie Algebra write by Minoru Wakimoto. This book was released on 2001. Lectures on Infinite-dimensional Lie Algebra available in PDF, EPUB and Kindle. 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 and 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.
Introduction to Finite and Infinite Dimensional Lie (Super)algebras
Introduction to Finite and Infinite Dimensional Lie (Super)algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Finite and Infinite Dimensional Lie (Super)algebras write by Neelacanta Sthanumoorthy. This book was released on 2016-04-26. Introduction to Finite and Infinite Dimensional Lie (Super)algebras available in PDF, EPUB and Kindle. 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
