Overview
- Offers a modern and systematic treatment of the classical structure theory of Hopf algebras
- Covers the general theory and a wide range of classical and recent applications
- Written by one of the founders of the theory together with an expert in its most recent developments
Part of the book series: Algebra and Applications (AA, volume 29)
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Table of contents (10 chapters)
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Front Matter
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General Theory
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Front Matter
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Applications
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Front Matter
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Back Matter
Keywords
About this book
The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results.
Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
Reviews
“Each chapter contains a final section with bibliographical indications; these sections contain a lot of history and philosophy of the subject, making the book very attractive to mathematicians who already have a Hopf algebra background. … the book is written in a self-contained way, making it suitable as a textbook for seminars and even master courses. … a welcome addition to the bookshelf of any Hopf algebraist.” (Stefaan Caenepeel, Mathematical Reviews, January, 2023)
Authors and Affiliations
About the authors
Frédéric Patras, alumnus of the Ecole Normale Supérieure and research director at CNRS, is an expert in the theory of Hopf algebras and their applications in analysis, combinatorics, Lie theory, probability, theoretical chemistry and physics. He has published and edited over a hundred works on various subjects.
Bibliographic Information
Book Title: Classical Hopf Algebras and Their Applications
Authors: Pierre Cartier, Frédéric Patras
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-3-030-77845-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-77844-6Published: 21 September 2021
Softcover ISBN: 978-3-030-77847-7Published: 22 September 2022
eBook ISBN: 978-3-030-77845-3Published: 20 September 2021
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: XV, 268
Number of Illustrations: 7 b/w illustrations
Topics: Algebra, Algebraic Topology, Group Theory and Generalizations