My motivation for studying Hopf algebras is twofold:

  • I'm interested in representation theory and the algebraic structure of group rings.
  • I will also take a course on algebraic groups soon and I think it would be helpful to know about Hopf algebras for that.

So I'm looking for a good introductory book on Hopf algebras for self-study and especially for one that has many examples and applications to the two topics mentioned above.

(As for my background, I know abstract algebra, commutative algebra and non-commutative algebra at a basic graduate level, I'm familiar with the basics on representation theory of (mostly finite) groups and category theory (including monoidal and symmetric monoidal, but not braided monoidal categories) and have some rudimentary knowledge of algebraic geometry. I know almost nothing about Lie algebras.)

  • 2
    $\begingroup$ Waterhouse's Introduction to Affine Group Schemes has some basic results about Hopf algebras, and (as far as I can remember) all the results needed about Hopf algebras are proved in the text. $\endgroup$
    – Joppy
    Feb 15, 2018 at 9:37
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    $\begingroup$ Quantum groups by Kassel is great, very easy to read. $\endgroup$ Feb 16, 2018 at 23:53
  • $\begingroup$ @NicolasHemelsoet do I need to know Lie algebras for that? $\endgroup$ Feb 16, 2018 at 23:59
  • $\begingroup$ No. There is even a chapter recalling basics about tensor products, etc... $\endgroup$ Feb 17, 2018 at 0:00
  • 1
    $\begingroup$ This is not the first time this question has been asked. $\endgroup$ Feb 18, 2018 at 3:29

1 Answer 1


Fundamentals of Hopf Algebras by Underwood.


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