Fundamentals of Hopf Algebras [electronic resource] / by Robert G. Underwood. - XIV, 150 p. 21 illus. online resource. - Universitext, 0172-5939 . - Universitext, .

Preface -- Notation -- 1. Algebras and Coalgebras -- 2. Bialgebras -- 3. Hopf Algebras -- 4. Applications of Hopf Algebras -- Bibliography.

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.

9783319189918

10.1007/978-3-319-18991-8 doi

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