The Connection Between Hopf Algebras and Groups

Hopf algebras are known to have a copious ammounts of structure which makes them useful in studying representations while, on the other hand, groups come equipt with little structure. In the following we will “realize” Hopf algebras as groups and comment on why we call quasitriangular Hopf algebras quantum groups. Hopefully, this will help demistify the confusion that comes along when studying Hopf algebras. For those of you who don’t know Hopf algebras, don’t worry! We will review them as well.

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The Arithmetic of Polynomial Rings over Finite Fields

Today we’re going to talk about something quite exciting and unexpected: the arithmetic of polynomial rings over finite fields and its similarity to the arithmetic of the integers. We’ll first run though some preliminary observations about the arithmetic of the polynomial rings which will suggest that it behaves similar to the arithmetic of the integers.

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