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＜電子ブック＞
Classical Hopf Algebras and Their Applications / by Pierre Cartier, Frédéric Patras
(Algebra and Applications. ISSN:21922950 ; 29)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XV, 268 p. 7 illus : online resource
著者標目	*Cartier, Pierre author Patras, Frédéric author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic topology LCSH:Group theory FREE:Algebra FREE:Algebraic Topology FREE:Group Theory and Generalizations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-77845-3

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