Classical Hopf Algebras and Their Applicat...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Pierre Cartier is a member of the IHES, alumnus of the Ecole Normale Supérieure and former research director at CNRS. A long associate of the Bourbaki group, he is known for his wide range of interests and contributions, among others in algebraic geometry, representation theory and mathematical physics. He is one of the founders of the theory of coalgebras and Hopf algebras.

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	284
Reihe:	Algebra and Applications
Inhalt:	xv 268 S. 7 s/w Illustr. 268 p. 7 illus.
ISBN-13:	9783030778446
ISBN-10:	3030778444
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Patras, Frédéric Cartier, Pierre
Auflage:	1st ed. 2021
Hersteller:	Springer International Publishing Algebra and Applications
Maße:	241 x 160 x 21 mm
Von/Mit:	Frédéric Patras (u. a.)
Erscheinungsdatum:	21.09.2021
Gewicht:	0,594 kg

preigu-id: 119946379