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Classical lie algebras at infinity

Record Type:	Electronic resources : Monograph/item
Title/Author:	Classical lie algebras at infinityby Ivan Penkov, Crystal Hoyt.
Author:	Penkov, Ivan.
other author:	Hoyt, Crystal.
Published:	Cham :Springer International Publishing :2022.
Description:	xiii, 239 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Lie algebras.
Online resource:	https://doi.org/10.1007/978-3-030-89660-7
ISBN:	9783030896607$q(electronic bk.)

Classical lie algebras at infinity
Penkov, Ivan.

Classical lie algebras at infinity[electronic resource] /by Ivan Penkov, Crystal Hoyt. - Cham :Springer International Publishing :2022. - xiii, 239 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

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.

ISBN: 9783030896607$q(electronic bk.)

Standard No.: 10.1007/978-3-030-89660-7doiSubjects--Topical Terms:

191078
Lie algebras.

LC Class. No.: QA252.3 / .P46 2022

Dewey Class. No.: 512.482

Classical lie algebras at infinity
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520 $a 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.
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