Modified traces for quasi-Hopf algebras
Abstract
Let H be a finite-dimensional unimodular pivotal quasi-Hopf algebra over a field k, and let H-mod be the pivotal tensor category of finite-dimensional H-modules. We give a bijection between left (resp. right) modified traces on the tensor ideal H-pmod of projective modules and left (resp. right) cointegrals for H. The non-zero left/right modified traces are non-degenerate, and we show that non-degenerate left/right modified traces can only exist for unimodular H. This generalises results of Beliakova, Blanchet, and Gainutdinov from Hopf algebras to quasi-Hopf algebras. As an example we compute cointegrals and modified traces for the family of symplectic fermion quasi-Hopf algebras.
Keywords
Cite
@article{arxiv.1812.10445,
title = {Modified traces for quasi-Hopf algebras},
author = {Johannes Berger and Azat M. Gainutdinov and Ingo Runkel},
journal= {arXiv preprint arXiv:1812.10445},
year = {2020}
}
Comments
21 pages; generalized Lemma 3.7 to the non-unimodular setting