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＜電子ブック＞
Classical Lie Algebras at Infinity / by Ivan Penkov, Crystal Hoyt
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XIII, 239 p : online resource
著者標目	*Penkov, Ivan author Hoyt, Crystal author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Algebra FREE:Topological Groups and Lie Groups FREE:Algebra
一般注記	Preface -- Notation and Terminology. - I. Structure of Locally Reductive Lie Algebras -- 1. Finite-dimensional Lie algebras -- 2. Finite-dimensional Lie superalgebras -- 3. Root-reductive Lie algebras -- 4. Two generalizations -- 5. Splitting Borel subalgebras of sl(infinity), frak o (infinity), sp(infinity) and generalized flags -- 6. General Cartan, Borel and parabolic subalgebras of gl(infinity) and sl(infinity) -- II. Modules over Locally Reductive Lie Algebras -- 7. Tensor modules of sl(infinity), frak o(infinity), sp (infinity) -- 8. Weight modules -- 9.Generalized Harish-Chandra modules -- III. Geometric aspects. - 10.The Bott-Borel-Weil Theorem -- References -- Index of Notation -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-030-89660-7

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