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Classical Hopf Algebras and Their Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Classical Hopf Algebras and Their Applications/ by Pierre Cartier, Frédéric Patras.
作者:	Cartier, Pierre.
其他作者:	Patras, Frédéric.
面頁冊數:	XV, 268 p. 7 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Group Theory and Generalizations. -
電子資源:	https://doi.org/10.1007/978-3-030-77845-3
ISBN:	9783030778453

Classical Hopf Algebras and Their Applications
Cartier, Pierre.

Classical Hopf Algebras and Their Applications[electronic resource] /by Pierre Cartier, Frédéric Patras. - 1st ed. 2021. - XV, 268 p. 7 illus.online resource. - Algebra and Applications,292192-2950 ;. - Algebra and Applications,20.

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.

ISBN: 9783030778453

Standard No.: 10.1007/978-3-030-77845-3doiSubjects--Topical Terms:

672112
Group Theory and Generalizations.

LC Class. No.: QA150-272

Dewey Class. No.: 512

Classical Hopf Algebras and Their Applications
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