Classical Hopf algebras and their applications / Pierre Cartier, Frédéric Patras.
2021
QA613.8 .C37 2021
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Title
Classical Hopf algebras and their applications / Pierre Cartier, Frédéric Patras.
ISBN
9783030778453 (electronic bk.)
3030778452 (electronic bk.)
9783030778446
3030778444
3030778452 (electronic bk.)
9783030778446
3030778444
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations
Item Number
10.1007/978-3-030-77845-3 doi
Call Number
QA613.8 .C37 2021
Dewey Decimal Classification
512/.55
Summary
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 5, 2021).
Added Author
Patras, Frédéric, author.
Series
Algebras and applications ; v. 29. 2192-2950
Available in Other Form
Classical Hopf algebras and their applications.
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Table of Contents
1. Introduction
Part I General Theory
2 Coalgebras, Duality
3. Hopf Algebras and Groups
4. Structure Theorems
5. Graded Hopf Algebras and the Descent Gebra
6. PreLie Algebras
Part II Applications
7. Group Theory
8. Algebraic Topology
9. Combinatorial Hopf Algebras
10. Renormalization.
Part I General Theory
2 Coalgebras, Duality
3. Hopf Algebras and Groups
4. Structure Theorems
5. Graded Hopf Algebras and the Descent Gebra
6. PreLie Algebras
Part II Applications
7. Group Theory
8. Algebraic Topology
9. Combinatorial Hopf Algebras
10. Renormalization.