Bibliograph

Classical Hopf Algebras and Their Applications, by Pierre Cartier, Frédéric Patras

Type

Label

Classical Hopf Algebras and Their Applications, by Pierre Cartier, Frédéric Patras

Language

eng

resource.imageBitDepth

Literary Form

non fiction

Main title

Classical Hopf Algebras and Their Applications

Medium

electronic resource

Nature of contents

dictionaries

Oclc number

1268984458

Responsibility statement

by Pierre Cartier, Frédéric Patras

Series statement

Algebra and Applications,, 29, 2192-2950Springer eBooks.

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.--, Provided by publisher

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

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