Representations of algebraic quantum groups and reconstruction theorems for tensor categories

摘要: We give a pedagogical survey of those aspects the abstract representation theory quantum groups which are related to Tannaka-Krein reconstruction problem. show that every concrete semisimple tensor *-category with conjugates is equivalent category finite dimensional non-degenerate *-representations discrete algebraic group. Working in self-dual framework groups, we then relate this earlier results S. L. Woronowicz and Yamagami. establish relation between braidings R-matrices context. Our approach emphasizes role natural transformations embedding functor. Thanks semisimplicity our categories emphasis on representations rather than corepresentations, proof more direct conceptual previous reconstructions. As special case, reprove classical result for compact groups. It only here analytic enter, otherwise proceed purely way. In particular, existence Haar functional reduced well known general concerning multiplier Hopf *-algebras.