A categorical and diagrammatical approach to Temperley-Lieb algebras
Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.
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arXiv subjects
Shigeru Yamagami
Publications and source records attributed to Shigeru Yamagami.
Notes on Operator Categories
The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules.
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Free Products of Semisimple Tensor Categories
Free products of semisimple tesnor categories are constructed with the help of polygonal presentation. The semisimplicity criterion is obtained for the Bisch-Jones' planar algebras as a byproduct.
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Tannaka Duals in Semisimple Tensor Categories
Tannaka duals of Hopf algebras inside semisimple tensor categories are used to construct orbifold tensor categories, which are shown to include the Tannaka dual of the dual Hopf algebras. The second orbifolds are then canonically isomorphic to the initial tensor categories.
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C*-tensor categories and free product bimodules
A C*-tensor category with simple unit object is realized by von Neumann algebra bimodules of finite Jones index if and only if it is rigid.
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