Finitely semisimple spherical categories and modular categories are self-dual

Details Finitely semisimple spherical categories and modular categories are self-dual Finitely semisimple spherical categories and modular categories are self-dual

2008-06-18

arxiv.org/abs/0806.2903v2

Advances in Mathematics 221 No. 5 (2009) 1608-1652

Mathematics

Quantum Algebra

42 pages; LaTeX with xypic macros; v2: typos corrected

Scientific paper

10.1016/j.aim.2009.03.002

We show that every essentially small finitely semisimple k-linear additive spherical category in which k=End(1) is a field, is equivalent to its dual over the long canonical forgetful functor. This includes the special case of modular categories. In order to prove this result, we show that the universal coend of the spherical category with respect to the long forgetful functor is self-dual as a Weak Hopf Algebra.

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