Categorical dualtiy for Yetter-Drinfeld C*-algebras. Beyond the braided-commutative case
Operator Algebras
2026-03-16 v2 Quantum Algebra
Abstract
We develop a tensor categorical duality in the sprit of the Tannaka-Krein duality for the C*-algebras admitting the Yetter-Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G, the Yetter-Drinfeld G-C*-algebras correspond to the bimodule categories over the representation category Rep(G), satisfying a certain centrality condition.
Keywords
Cite
@article{arxiv.2504.21162,
title = {Categorical dualtiy for Yetter-Drinfeld C*-algebras. Beyond the braided-commutative case},
author = {Lucas Hataishi and Makoto Yamashita},
journal= {arXiv preprint arXiv:2504.21162},
year = {2026}
}
Comments
19 pages, split off part of arXiv:2205.06663 as a separate paper