Fundamentals of Hopf Algebras
Underwood, Robert G.
creator
author.
SpringerLink (Online service)
text
gw
2015
monographic
eng
access
XIV, 150 p. 21 illus. online resource.
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises. Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.
Preface -- Notation -- 1. Algebras and Coalgebras -- 2. Bialgebras -- 3. Hopf Algebras -- 4. Applications of Hopf Algebras -- Bibliography.
by Robert G. Underwood.
Mathematics
Associative rings
Rings (Algebra)
Commutative algebra
Commutative rings
Computer science
Mathematics
Computer mathematics
Number theory
Mathematics
Associative Rings and Algebras
Commutative Rings and Algebras
Number Theory
Mathematical Applications in Computer Science
QA251.5
512.46
Springer eBooks
Universitext
9783319189918
http://dx.doi.org/10.1007/978-3-319-18991-8
http://dx.doi.org/10.1007/978-3-319-18991-8
150610
20180115171634.0
978-3-319-18991-8