Overview
- Assembles the available tools and methods in a new, coherent theory, building from foundational material
- Invites the reader to explore a wide open research area
- Provides thought-provoking mixture of mathematical ideas
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (10 chapters)
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Front Matter
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Part I
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Front Matter
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Part III
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“The book is self-contained in an introductory way, it would be better for the reader to know the basics of Lie algebras and their representations. … the book is most suitable for advanced graduate students and research mathematicians.” (Chengkang Xu, Mathematical Reviews, October, 2022)
“Classical Lie Algebras at Infinity is a very interesting book by I. Penkov and C. Hoyt. … Plenty of exercises of various levels of difficulty and open problems are given throughout the book. This exposition is an invitation to a wide open area of research, aiming to invoke a complex combination of advanced mathematical ideas.” (Mee Seong Im, zbMATH 1490.17025, 2022)
“The book is designed to not only serve as a reference but also to introduce well-prepared people to the subject and its current areas of inquiry. … it seems fair to say that this book will appeal to a somewhat narrower subset of readers of this column than do many of the books reviewed here. But the people in this subset should find this a useful, in the authors’ words, ‘invitation to a wide open research area’.” (Mark Hunacek, MAA Reviews, August 1, 2022)Authors and Affiliations
Bibliographic Information
Book Title: Classical Lie Algebras at Infinity
Authors: Ivan Penkov, Crystal Hoyt
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-89660-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-89659-1Published: 06 January 2022
Softcover ISBN: 978-3-030-89662-1Published: 07 January 2023
eBook ISBN: 978-3-030-89660-7Published: 05 January 2022
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIII, 239
Topics: Topological Groups, Lie Groups, Algebra