Tannaka theory and the FRT construction over non-commutative algebras

Kenichi Shimizu

Tannaka theory and the FRT construction over non-commutative algebras

Quantum Algebra 2021-07-06 v2 Category Theory Rings and Algebras

Authors: Kenichi Shimizu

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.

Keywords

tannaka theory frt construction bialgebroid coquasitriangular bimonad hopf algebroid non-commutative algebra

Cite

@article{arxiv.1912.13160,
  title  = {Tannaka theory and the FRT construction over non-commutative algebras},
  author = {Kenichi Shimizu},
  journal= {arXiv preprint arXiv:1912.13160},
  year   = {2021}
}

Comments

v2, 56 pages, 118 picture files. Fully revised. The invertibility of the lax braiding of FRT bialgebroids is discussed. A relation to Hayashi's construction of face algebras is added

Tannaka theory and the FRT construction over non-commutative algebras

Abstract

Keywords

Cite

Comments

Related papers