Fundamentals of Hopf Algebras

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book Fundamentals of Hopf Algebras by Robert G. Underwood, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Robert G. Underwood ISBN: 9783319189918
Publisher: Springer International Publishing Publication: June 10, 2015
Imprint: Springer Language: English
Author: Robert G. Underwood
ISBN: 9783319189918
Publisher: Springer International Publishing
Publication: June 10, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Advances in Personalized Web-Based Education by Robert G. Underwood
Cover of the book Fuzzy Logic Augmentation of Nature-Inspired Optimization Metaheuristics by Robert G. Underwood
Cover of the book Robustness in Econometrics by Robert G. Underwood
Cover of the book The Evolution and Everyday Practice of Collective Patient Involvement in Europe by Robert G. Underwood
Cover of the book Computer Science – Theory and Applications by Robert G. Underwood
Cover of the book Social Choice and Democratic Values by Robert G. Underwood
Cover of the book Multidisciplinary Management of Rectal Cancer by Robert G. Underwood
Cover of the book Computational Problems in Engineering by Robert G. Underwood
Cover of the book Communicating National Image through Development and Diplomacy by Robert G. Underwood
Cover of the book Transionospheric Synthetic Aperture Imaging by Robert G. Underwood
Cover of the book Radiation Therapy for Liver Tumors by Robert G. Underwood
Cover of the book Juana I by Robert G. Underwood
Cover of the book Modern Sensing Technologies by Robert G. Underwood
Cover of the book Surplus Analysis of Sparre Andersen Insurance Risk Processes by Robert G. Underwood
Cover of the book Membrane Potential Imaging in the Nervous System and Heart by Robert G. Underwood
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy