Tannaka theory and the FRT construction over non-commutative algebras

Kenichi Shimizu

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arXiv · 1912.13160

Tannaka theory and the FRT construction over non-commutative algebras

Kenichi Shimizu

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Abstract

Let $A$ be an algebra over a commutative ring $k$. We introduce the notion of a coquasitriangular left bialgebroid over $A$ and show that the category of left comodules over such a bialgebroid has a braiding. We also investigate a Tannaka type construction of bimonads and bialgebroids. As an application, the Faddeev-Reshetikhin-Takhtajan (FRT) construction over the algebra $A$ is established. Our construction associates a coquasitriangular bialgebroid to a braided object $(M, c)$ in the category of $A$-bimodules such that $M$ is finitely generated and projective as a left $A$-module. A Hopf algebroid version of this construction is also provided.

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Kenichi Shimizu. 2019-12-31. Tannaka theory and the FRT construction over non-commutative algebras. https://arxiv.org/abs/1912.13160

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