Hopf Algebras and Their Actions on Rings by Susan Montgomery (PDF)

Description

The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange’s theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Used this for a graduate independent study on Hopf Algebras. Was pretty great, and uses group algebras as a guiding / recurring example which helps a lot. Still, it takes some staring at a few lines to figure out the reasoning but that’s only natural.

⭐That’s the excellent book i have ever read on the subject of hopf algebra. It’s definitely worth buying it.

⭐

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