UID:
almahu_9949177485002882
Umfang:
XV, 268 p. 7 illus.
,
online resource.
Ausgabe:
1st ed. 2021.
ISBN:
9783030778453
Serie:
Algebra and Applications, 29
Inhalt:
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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783030778446
Weitere Ausg.:
Printed edition: ISBN 9783030778460
Weitere Ausg.:
Printed edition: ISBN 9783030778477
Sprache:
Englisch
DOI:
10.1007/978-3-030-77845-3
URL:
https://doi.org/10.1007/978-3-030-77845-3
