The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results.
Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
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"Each chapter contains a final section with bibliographical indications; these sections contain a lot of history and philosophy of the subject, making the book very attractive to mathematicians who already have a Hopf algebra background. ... the book is written in a self-contained way, making it suitable as a textbook for seminars and even master courses. ... a welcome addition to the bookshelf of any Hopf algebraist." (Stefaan Caenepeel, Mathematical Reviews, January, 2023)