Chelsea Walton

Cover art by Jean Tashima

A free version of Volume 1 is available [here].
Enjoy this textbook?
Citations and library requests are appreciated!

Volume 1 is available for purchase...
Via the 619 Wreath website at a discount.
Also available on Amazon (US only),
and on Google Play.

Welcome! I am happy that you are here, and I am excited to present to you a topic that I have enjoyed over the last several years. My journey towards landing on this topic began in graduate school, where I studied material related to the first chapter of this book (namely, algebras over a field). Later as a faculty member, I encountered the material comprising the remaining chapters here, discovering the world of Algebraic Quantum Symmetry. I’ve found all of the structures in this field quite beautiful and important in their own way.

Volume 1 pertains to algebras and categories: Chapter 1 is on algebras over a field; Chapter 2 is on category theory; Chapter 3 is on monoidal categories; and Chapter 4 is on algebras in monoidal categories.

Volume 2 will be on coalgebras and Frobenius algebras: Chapter 5 will be on coalgebras over a field; Chapter 6 will be on coalgebras in monoidal categories; Chapter 7 will be on Frobenius algebras over a field; and Chapter 8 will be on Frobenius algebras in monoidal categories.

Volume 3 will be on Hopf algebras and beyond: Chapter 9 will be on bialgebras and Hopf algebras over a field; Chapter 10 will be on braided monoidal categories; Chapter 11 will be on Hopf algebras and related structures in monoidal categories; and Chapter 12 will be on higher categorical structures.

Updates and corrections for Volume 1: [Found here]

Bibliographic information:
C. Walton. Symmetries of Algebras, Vol. 1. 619 Wreath Publishing, Oklahoma City, OK, 2024.

ISBN numbers: 978-1-958469-21-7 (hardcover);
978-1-958469-20-0 (paperback); 978-1-958469-26-2 (e-book).

AMS Mathematical Reviews (MathSciNet): MR4806154

Comments are welcome via email.

Mailing Address

Email