26 citations · 54 across the 15 of their papers we have counts for
15 papers
Equivariant Eilenberg-Watts theorem for module coalgebras
Taiki Shibata, Kenichi Shimizu
For coalgebras and , Takeuchi proved that the category of linear functors from to preserving small coproducts is equivalent to the category…
Exact module categories over
Daisuke Nakamura, Taiki Shibata, Kenichi Shimizu
We give a complete list of indecomposable exact module categories over the finite tensor category of representations of the small quantum group…
Pointed Hopf superalgebras of dimension up to 10
Taiki Shibata, Kenichi Shimizu, Ryota Wakao
By utilizing the technique introduced in our previous work to construct Hopf superalgebras by an inverse procedure of the Radford-Majid bosonization, we classify non-semisimple poi…
On classification of Hopf superalgebras of low dimension
Taiki Shibata, Ryota Wakao
We examine the inverse procedure of the Radford-Majid bosonization for Hopf superalgebras and give a handy method for enumerating Hopf superalgebras whose bosonization is isomorphi…
Frobenius kernels of algebraic supergroups and Steinberg's tensor product theorem
Taiki Shibata
For a split quasireductive supergroup defined over a field, we study structure and representation of Frobenius kernels of and we give a necessary and sufficient condi…
Nakayama functors for coalgebras and their applications to Frobenius tensor categories
Taiki Shibata, Kenichi Shimizu
We introduce Nakayama functors for coalgebras and investigate their basic properties. These functors are expressed by certain (co)ends as in the finite case discussed by Fuchs, Sch…
Affine Kac-Moody groups and Lie algebras in the language of SGA3
Jun Morita, Arturo Pianzola, Taiki Shibata
In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groups play a distinguished role due to their many applications to various areas of mathematics and physic…
Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations
Jun Morita, Arturo Pianzola, Taiki Shibata
We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations.
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…
Affine algebraic super-groups with integral
Akira Masuoka, Taiki Shibata, Yuta Shimada
We generalize to the super context, the known fact that if an affine algebraic group over a commutative ring acts freely (in an appropriate sense) on an affine scheme o…
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…
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…
On functor points of affine supergroups
Akira Masuoka, Taiki Shibata
To construct an affine supergroup from a Harish-Chandra pair, Gavarini [2] invented a natural method, which first constructs a group functor and then proves that it is representabl…
Hyperfine spin qubits in irradiated malonic acid: heat-bath algorithmic cooling
Daniel K. Park, Guanru Feng, Robabeh Rahimi +7
The ability to perform quantum error correction is a significant hurdle for scalable quantum information processing. A key requirement for multiple-round quantum error correction i…
Algebraic supergroups and Harish-Chandra pairs over a commutative ring
Akira Masuoka, Taiki Shibata
We prove a category equivalence between algebraic supergroups and Harish-Chandra pairs over a commutative ring which is -torsion free. The result is applied to re-construct the…