3 papers
math.QA2021
Modified traces and the Nakayama functor
Taiki Shibata, Kenichi Shimizu
We organize the modified trace theory with the use of the Nakayama functor of finite abelian categories. For a linear right exact functor on a finite abelian category $\mathcal…
math.QA2018
Categorical aspects of cointegrals on quasi-Hopf algebras
Taiki Shibata, Kenichi Shimizu
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-Ho…
math.RT2018
Borel-Weil Theorem for Algebraic Supergroups
Taiki Shibata
We study the structure of an algebraic supergroup and establish the Borel-Weil theorem for to give a systematic construction of all simple supermodules ov…