Hopf Algebras

An introduction to the basic theory of Hopf algebras for those familiar with basic linear and commutative algebra.

Eiichi Abe (Author)

9780521604895, Cambridge University Press

Paperback, published 3 June 2004

300 pages
21.5 x 13.7 x 1.6 cm, 0.399 kg

The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivan's proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.

Preface
Notation
1. Modules and algebras
2. Hopf algebras
3. Hopf algebras and representations of groups
4. Applications to algebraic groups
5. Applications to field theory
Appendix
References
Index.

Subject Areas: Applied mathematics [PBW]