Quantum Groups and Hopf Algebras

GASTÓN ANDRÉS GARCÍA

São Pedro, São Paulo, Brasil

Congreso; XVII Coloquio Latinoamericano de Álgebra; 2009

Universidad de São Paulo

These notes correspond to a mini-course for graduate and undergraduate students given in the XVIII Latin American Algebra Colloquium in S~ao Pedro, Brazil. Because of the lenght of the course, we intend only to give the basic ideas of the subject and to show, by means of examples, how quantum groups enter into the scene of the classi cation problem of nite-dimensional Hopf algebras over an algebraically closed eld of characteristic zero. The reader who is interested in this subject may have a look at the bibliography on quantum groups and Hopf algebras and references therein. We did not intend to give an exhaustive or comprehensive list of the references, but just give some of them to serve as a guide.