| Dewey Class |
512 |
| Titel |
Classical Hopf Algebras and Their Applications ([EBook] /) / by Pierre Cartier, Frédéric Patras. |
| Verfasser |
Cartier, Pierre |
| Added Personal Name |
Patras, Frédéric |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2021. |
| Veröffentl |
Cham : : Springer International Publishing : : Imprint: Springer, , 2021. |
| Physical Details |
XV, 268 p. 7 illus. : online resource. |
| Reihe |
Algebra and Applications 2192-2950 ; ; 29 |
| ISBN |
9783030778453 |
| Summary Note |
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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-77845-3 |
| LINKS ZU 'VERWANDTEN WERKEN |
Schlagwörter: .
Algebra .
Algebraic Topology .
Group theory .
Group Theory and Generalizations .
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