Centres, trace functors, and cyclic cohomology
Quantum Algebra
2022-11-14 v2 Category Theory
Rings and Algebras
Abstract
We study the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence to anti Yetter-Drinfel'd contramodules and anti Yetter-Drinfel'd modules, respectively. This is directly connected to the existence of a trace functor on the monoidal categories of modules and comodules in question, which in turn allows to recover (or define) cyclic operators enabling cyclic cohomology.
Cite
@article{arxiv.2012.13790,
title = {Centres, trace functors, and cyclic cohomology},
author = {Niels Kowalzig},
journal= {arXiv preprint arXiv:2012.13790},
year = {2022}
}
Comments
41 pages; v2: added a subsection which better elucidates how trace functors emerge in biclosed categories; various minor improvements. To appear in Comm. Contemp. Math