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Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace
[article]
1999
arXiv
pre-print
If A is a weak C^*-Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C^*-category with monoidal unit being the GNS representation D_eps associated to the counit . This category has isomorphic left dual and right dual objects which leads, as usual, to the notion of dimension function. However, if is not pure the dimension function is matrix valued with rows and columns labelled by the irreducibles contained in D_eps. This happens precisely when the
arXiv:math/9906045v1
fatcat:6z5yxbkhengi3bn5w7bglcon6q