Mathematics – Quantum Algebra
Scientific paper
2007-11-09
Journal of Algebra 321 No. 12 (2009) 3714-3763
Mathematics
Quantum Algebra
52 pages; LaTeX2e; xypic and pstricks macros; v2: typos corrected
Scientific paper
10.1016/j.jalgebra.2009.02.026
We show that every modular category is equivalent as an additive ribbon category to the category of finite-dimensional comodules of a Weak Hopf Algebra. This Weak Hopf Algebra is finite-dimensional, split cosemisimple, weakly cofactorizable, coribbon and has trivially intersecting base algebras. In order to arrive at this characterization of modular categories, we develop a generalization of Tannaka-Krein reconstruction to the long version of the canonical forgetful functor which is lax and oplax monoidal, but not in general strong monoidal, thereby avoiding all the difficulties related to non-integral Frobenius-Perron dimensions.
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