On Unimodular Finite Tensor Categories
On Unimodular Finite Tensor Categories
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关于幺模有限张量范畴
DOI：
10.1093/imrn/rnv394
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发表时间：
2017
影响因子：
1
通讯作者：
Kenichi Shimizu
中科院分区：
文献类型：
--
作者：
Shimizu Kenichi;Kenichi Shimizu;Kenichi Shimizu
设是具有单单位对象的有限张量范畴，记它的么半心，设LandR是遗忘函子的左伴随和右伴随。我们证明了下列条件是等价的：(1)是么模，(2)U是Frobenius函子，(3)L保持对偶，(4)R保持对偶，(5)是自对偶，(6)是自对偶，其中是单位对象。我们还给出了其他一些等价条件。作为应用，我们给出了有限维么模Hopf代数的一些拓扑不变量的范畴理解。
Letbe a finite tensor category with simple unit object, letdenote its monoidal center, and letLandRbe a left adjoint and a right adjoint of the forgetful functor. We show that the following conditions are equivalent: (1)is unimodular, (2)Uis a Frobenius functor, (3)Lpreserves the duality, (4)Rpreserves the duality, (5)is self-dual, and (6)is self-dual, whereis the unit object. We also give some other equivalent conditions. As an application, we give a categorical understanding of some topological invariants arising from finite-dimensional unimodular Hopf algebras.