@article{38e65effff9747c0b38ffdd536e53959,
title = "Categorical aspects of cointegrals on quasi-Hopf algebras",
abstract = "We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Hopf algebra H, we give an explicit description of categorical cointegrals of the category MH of left H-modules in terms of cointegrals on H. Provided that H is unimodular, we also express the Frobenius structure of the {\textquoteleft}adjoint algebra{\textquoteright} in the Yetter-Drinfeld category YHHD by using an integral in H and a cointegral on H. Finally, we give a description of the twisted module trace for projective H-modules in terms of cointegrals on H.",
keywords = "Cointegral, Integral, Module trace, Quasi-Hopf algebra, Tensor category, Yetter-Drinfeld category",
author = "Taiki Shibata and Kenichi Shimizu",
note = "Funding Information: We are grateful to Peter Schauenburg for helpful discussion. We are also grateful to the referee for careful reading of the manuscript and several valuable suggestions. The first author (T.S.) is supported by JSPS KAKENHI Grant Number JP19K14517 . The second author (K.S.) is supported by JSPS KAKENHI Grant Numbers JP16K17568 and JP20K03520 . Publisher Copyright: {\textcopyright} 2020",
year = "2020",
month = dec,
day = "15",
doi = "10.1016/j.jalgebra.2020.08.012",
language = "English",
volume = "564",
pages = "353--411",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}