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Classical Hopf algebras and their ap...

Cartier, Pierre.

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Classical Hopf algebras and their applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Classical Hopf algebras and their applications/ by Pierre Cartier, Frederic Patras.
作者:	Cartier, Pierre.
其他作者:	Patras, Frederic.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xv, 268 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Hopf algebras. -
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, Frederic Patras. - Cham :Springer International Publishing :2021. - xv, 268 p. :ill., digital ;24 cm. - Algebra and applications,v.292192-2950 ;. - Algebra and applications ;v.29..

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:

706147
Hopf algebras.

LC Class. No.: QA613.8 / .C37 2021

Dewey Class. No.: 512.55

Classical Hopf algebras and their applications
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245 1 0 $a Classical Hopf algebras and their applications $h [electronic resource] / $c by Pierre Cartier, Frederic Patras.
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505 0 $a 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.
520 $a 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.
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