Categorical duality for Yetter-Drinfeld algebras
Abstract
We study tensor structures on (Rep G)-module categories defined by actions of a compact quantum group G on unital C*-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of G to the structure of a braided-commutative Yetter-Drinfeld algebra. This shows that the category of braided-commutative Yetter-Drinfeld G-C*-algebras is equivalent to the category of generating unitary tensor functors from Rep G into C*-tensor categories. To illustrate this equivalence, we discuss coideals of quotient type in C(G), Hopf-Galois extensions and noncommutative Poisson boundaries.
Keywords
Cite
@article{arxiv.1310.4407,
title = {Categorical duality for Yetter-Drinfeld algebras},
author = {Sergey Neshveyev and Makoto Yamashita},
journal= {arXiv preprint arXiv:1310.4407},
year = {2021}
}
Comments
24 pages; v3: the last section was split off as a separate manuscript arxiv:1405.6574, as it no longer relies on this paper, a converse to Tomatsu's result on Poisson boundaries added; v4: minor corrections, to appear in Doc Math