Publications

Research interest

• Hopf algebras and tensor categories

Papers

1. Kenichi Shimizu. Monoidal Morita invariants for finite groups. Journal of Algebra (323), pp. 397-418, 2010 [DOI:10.1016/j.jalgebra.2009.08.021]

2. Kenichi Shimizu. Frobenius-Schur indicators in Tambara-Yamagami categories. Journal of Algebra (332), pp. 543-564, 2011 [DOI:10.1016/j.jalgebra.2011.02.002]

3. Kenichi Shimizu. Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras. Algebras and Representation Theory (15), pp. 325-357, 2012 [DOI:10.1007/s10468-010-9243-5]

4. Kenichi Shimizu. On the linear independency of monoidal natural transformations. Proceedings of the American Mathematical Society (140), pp. 1939-1946, 2012 [DOI:10.1090/S0002-9939-2011-11068-2]

5. Kenichi Shimizu. Frobenius-Schur indicator for categories with duality. Axioms (1), 324-364, 2012 (in the special issue of Hopf Algebras, Quantum Groups and Yang-Baxter Equations) [DOI:10.3390/axioms1030324]

6. Kenichi Shimizu. On indicators of Hopf algebras. Israel Journal of Mathematics (207), 155-201, 2015 [DOI:10.1007/s11856-015-1156-x]

7. Kenichi Shimizu. The pivotal cover and Frobenius-Schur indicators. Journal of Algebra (428), pp. 357-402, 2015 [DOI:10.1016/j.jalgebra.2015.01.014]

8. Kenichi Shimizu and Michihisa Wakui. Schrödinger representations from the viewpoint of monoidal categories. Algebras and Representation Theory [DOI:10.1007/s10468-015-9554-7]

9. Kenichi Shimizu. On unimodular finite tensor categories. International Mathematics Research Notices, 2016 [DOI:10.1093/imrn/rnv394]

10. Kenichi Shimizu. The relative modular object and Frobenius extensions of finite Hopf algebras. Journal of Algebra, 2016 [DOI:10.1016/j.jalgebra.2016.09.017]

11. Kenichi Shimizu. The monoidal center and the character algebra.Journal of Pure and Applied Algebra, 2017 [10.1016/j.jpaa.2016.12.037]

12. Diogo Kendy Matsumoto and Kenichi Shimizu. Quiver-theoretical approach to dynamical Yang-Baxter maps. Journal of Algebra (507), pp. 47-80, 2018 [10.1016/j.jalgebra.2018.04.003]

13. Kenichi Shimizu. Integrals for finite tensor categories. Algebras and Representation Theory(22), pp. 459-453, 2019 [DOI:10.1007/s10468-018-9777-5]

14. Kenichi Shimizu. Non-degeneracy conditions for braided finite tensor categories. Advances in Mathematics [DOI:10.1016/j.aim.2019.106778]

15. Kenichi Shimizu. Further results on the structure of (co)ends in finite tensor categories. Applied Categorical Structures 28, pp. 237-286, 2020 [DOI:10.1007/s10485-019-09577-7]

16. Taiki Shibata and Kenichi Shimizu. Categorical aspects of cointegrals on quasi-Hopf algebras. Journal of Algebra (564), pp. 353-411, 2020 [DOI:10.1016/j.jalgebra.2020.08.012]

17. Taiki Shibata and Kenichi Shimizu. Modified Traces and the Nakayama Functor. Algebras and Representation Theory, 2021 [DOI:10.1007/s10468-021-10102-5]

18. Kenichi Shimizu. Pivotal structures of the Drinfeld center of a finite tensor category. Journal of Pure and Applied Algebra, 2023 [DOI:10.1016/j.jpaa.2023.107321, arXiv:1608.05905]

19. Kenichi Shimizu. Ribbon structures of the Drinfeld center of a finite tensor category. Kodai Mathematical Journal, 2023 [DOI:10.2996/kmj46106, arXiv:1707.09691]

20. Taiki Shibata and Kenichi Shimizu. Nakayama functors for coalgebras and their applications for Frobenius tensor categories. Advances in Mathematics, 2023 [10.1016/j.aim.2023.108960, arXiv:2110.08739]

Preprints

1. Kenichi Shimizu. Relative Serre functor for comodule algebras [arXiv:1904.00376]

2. Kenichi Shimizu. Tannaka theory and the FRT construction over non-commutative algebras [arXiv:1912.13160]

3. Kenichi Shimizu. Nakayama functor for monads on finite abelian categories [arXiv:2208.08203]

4. Taiki Shibata and Kenichi Shimizu. Exact sequences of Frobenius tensor categories [arXiv:2303.14687]

Proceedings

1. Kenichi Shimizu. Frobenius properties of tensor functors. Toyama Mathematical Journal 37, 2015

2. Kenichi Shimizu. Recent developments of the categorical Verlinde formula, in: "Proceedings of the Meeting for Study of Number Theory, Hopf algebras and Related Topoics" edited by H. Yamane, T. Kogiso, Y. Koga and I. Kimura, Yokohama Publ., 2019, pp. 197-222.

3. Kenichi Shimizu. Hopf algebraic methods in finite tensor categories: Characters and integrals [10.1090/conm/771/15516]

Conference Talks (selected)

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