A Course on Hopf Algebras (eBook, PDF)
Rinat Kashaev
eBook, PDF

A Course on Hopf Algebras (eBook, PDF)

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This textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang-Baxter equations.Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel'd's quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows...

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