Mathematics – Quantum Algebra
Scientific paper
2002-03-20
Alg. Repres. Theor. 7, 517-573 (2004)
Mathematics
Quantum Algebra
Latex2e, 43 pages. Uses diagrams.tex V3.88
Scientific paper
We give a pedagogical survey of those aspects of the abstract representation theory of quantum groups which are related to the Tannaka-Krein reconstruction problem. We show that every concrete semisimple tensor *-category with conjugates is equivalent to the category of finite dimensional non-degenerate *-representations of a discrete algebraic quantum group. Working in the self-dual framework of algebraic quantum groups, we then relate this to earlier results of S. L. Woronowicz and S. Yamagami. We establish the relation between braidings and R-matrices in this context. Our approach emphasizes the role of the natural transformations of the embedding functor. Thanks to the semisimplicity of our categories and the emphasis on representations rather than corepresentations, our proof is more direct and conceptual than previous reconstructions. As a special case, we reprove the classical Tannaka-Krein result for compact groups. It is only here that analytic aspects enter, otherwise we proceed in a purely algebraic way. In particular, the existence of a Haar functional is reduced to a well known general result concerning discrete multiplier Hopf *-algebras.
Mueger Michael
Roberts John E.
Tuset Lars
No associations
LandOfFree
Representations of algebraic quantum groups and reconstruction theorems for tensor categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Representations of algebraic quantum groups and reconstruction theorems for tensor categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of algebraic quantum groups and reconstruction theorems for tensor categories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-495223