Format:
1 Online-Ressource (XV, 268 p. 7 illus.)
ISBN:
9783030778453
Series Statement:
Algebra and Applications 29
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783030778446
Additional Edition:
ISBN 9783030778460
Additional Edition:
ISBN 9783030778477
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030778446
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030778460
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030778477
Additional Edition:
Erscheint auch als Druck-Ausgabe Cartier, Pierre, 1932 - Classical Hopf algebras and their applications Cham, Switzerland : Springer Nature, 2021 ISBN 9783030778446
Additional Edition:
ISBN 9783030778477
Language:
English
Subjects:
Mathematics
Keywords:
Hopf-Algebra
;
Algebraische Kombinatorik
;
Einhüllende Algebra
;
Deformation
;
Renormierung
DOI:
10.1007/978-3-030-77845-3
