Classical Hopf Algebras and Their Applications Algebra and Applications 29 Pierre Cartier Frédéric Patras

Classical Hopf Algebras and Their Applications Algebra and Applications 29 Pierre Cartier Frédéric Patras – Ebook PDF Instant Download/Delivery ISBN(s):3030778444, 9783030778446

Product details:

• ISBN 10: 3030778444
• ISBN 13: 9783030778446
• Author: Pierre Cartier, Frédéric Patras

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.

Table contents:

1. Introduction
2. Part I. General Theory
3. Coalgebras, Duality
4. Hopf Algebras and Groups
5. Structure Theorems
6. Graded Hopf Algebras and the Descent Gebra
7.  Pre-lie Algebras
8. Part II. Applications
9. Group Theory
10. Algebraic Topology
11. Combinatorial Hopf Algebras, Twisted Structures, and Species
12. Renormalization

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