Hopf Algebras and Their Generalizations from a Category Theoretical Point of View: 2226 (Lecture Notes in Mathematics)

Book Details

• Publisher: Springer

• Author: Gabriella Böhm

• Language: English

• Edition: 1st ed. 2018

• ISBN: 9783319981369

• Pages: 165

• Cover: Paperback

• Format: Import

About the Book

Generalizations of Hopf Algebras: A Category-Theoretical Approach by Gabriella Böhm offers a self-contained introduction to the broad and rich theory of Hopf algebras and their generalizations. This book is designed for graduate students and researchers in algebra and category theory, providing a unified, category-theoretical perspective on these important mathematical structures.

Building upon the foundational work of Sweedler in the 1960s, this text explores how the multiplication of modules over Hopf algebras can be generalized through the use of more general monoidal categories. By broadening the scope of application, the book extends the utility of Hopf algebras into areas such as algebraic geometry, representation theory, and combinatorics.

The author covers various generalizations of Hopf algebras, including bialgebroids, weak bialgebras, and bimonoids in duoidal categories. Additionally, it introduces structures like bialgebras over commutative rings, semi-Hopf group algebras, and categories enriched in coalgebras. Each concept is explained with clarity, accompanied by numerous examples and exercises designed to deepen understanding.

The book is an ideal resource for anyone interested in the advanced study of algebraic structures, with detailed worked solutions to exercises allowing for effective self-study. Whether you're delving into category theory or seeking to explore the generalizations of Hopf algebras, this text serves as both an introduction and an advanced reference.