List of My Papers

(joint with Yuta Takahashi) Quotients in super-symmetry: formal supergroup case, Comm. Algebra; DOI: 10.1080/00927872.2024.2338492

Supersymmetric Picard-Vessiot theorey, preprint [arXiv2307.01997]

(joint with Takuya Oe, Yuta Takahashi)  Torsors in super-symmetry, preprint [arXiv2101.03461]

(joint with Alexandr Zubkov)  Group superschemes,  J. Algebra 605(2022),  89--145;  DOI: 10.1016/j.jalgebra.2022.04.027;  preprint [arXiv2011.14207]

(joint with Taiki Shibata, Yuta Shimada) Affine algebraic super-groups with integral,  Comm. Algebra 50 (2) (2022),  615--634;  DOI: 10.1080/00927872.2021.1963758;  preprint  [arXiv2003.05100]

(joint with Yuta Shimada) Twisted forms of differential Lie algebras over $\mathbb{C}(t)$ associated with complex simple Lie algebras, Arnold Math. Journal,   7 (2021),  107--134; DOI: 10.1007/s40598-020-00155-7; preprint [arXiv1912.10705  ]

(joint with Alexandr Zubkov) On the notion of Krull super-dimension, J. Pure Appl. Algebra 224 (2020), no.5, 106245; DOI: 10.1016/j.jpaa.2019.106245; preprint [arXiv1905.08219].

(joint with Yuta Takahashi) Geometric construction of G/H in supersymmetry, Transform. Groups 26(1) (2021), 347--375;  DOI: 10.1007/s00031-020-09583-3; preprint [arXiv1808.05753]; There is a typo in the preprint on arXiv: in the proof of Lemma 4.6, $\mathcal{S}_D$ should be replaced by $\mathcal{S}_C$.

(joint with Mitsukazu Hoshi, Yuta Takahashi) Hopf-algebraic techniques applied to super Lie groups over a complete field, J. Algebra 562 (2020), 28--93;  DOI: 10.1016/j.algebra.2020.06.019; preprint [arXiv1706.02839v3]

(joint with Atsuya Nakazawa) Simple modules over finite quantum groups and their Drinfel'd doubles, in: H. Yamane et al. eds., Proceedings of the Meeting for Study of Number Theory, Hopf Algebras and Related Topics, pp.81--104, Yokohama Publ., Yokohama, 2019; [arXiv1611.06325]

(joint with Katsunori Saito and Hiroshi Umemura) Toward quantization of Galois theory, Annales de la Fac. des Sciences de Toulouse,  Tome XXIX no.5 (2020), Volume à la mémoire de Hiroshi Umemura : “Équations de Painlevé et théories de Galois différentielles”, pp.1319--1431. 

(joint with Taiki Shibata) On functor points of affine supergroups, J. Algebra 503 (2018) 534--572; DOI: 10.1016/j.algebra.2018.02.0002; preprint [arXiv1505.06558]

(joint with Alexandr Zubkov) Solvability and nilpotency for algebraic supergroups, J. Pure Appl. Algebra 221 (2017),  339–365; DOI: 10.1016/j.jpaa.2016.06.012; preprint [arXiv1502.07021]

(joint with Christian Kassel) The Noether problem for Hopf algebras, J. Noncom. Geometry 10 (2016), 405-428; preprint [arXiv1404.4941]

Hopf algebraic techniques applied to super algebraic groups, Algebra Symposium Report 2013, Math. Soc. Japan;  preprint [arXiv1311.1261]

(joint with Atsushi Ishii) Handlebody-knot invariants derived from unimodular Hopf algebras, J. Knot Theory Ramifications 23 (2014), No. 7, 1460001, 24 pp; preprint [arXiv1307.5632]

(joint with Taiki Shibata) Algebraic supergroups and Harish-Chandra pairs over a commutative ring, Trans. AMS 369 (2017), 3443–3481; DOI: 10.1090/tran/6751; preprint  [arXiv1304.0531]

(joint with Makoto Yanagawa) $\times_R$-Bialgebras associated with iterative $q$-difference rings, Internat. J. Math. 24 (2013), no.4, 1350030, 27pp.; preprint [arXiv1301.1421]

(joint with Nicolas Andruskiewitsch, Ivan Angiono, Agustin Garcia Iglesias and Cristian Vay) Lifting via cocycle deformation, J. Pure Appl. Algebra 218 (2014), 684–703; preprint [arXiv1212.5279]

Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field, Transform. Groups 17 (2014), 1085--1121; preprint  [arXiv1111.2387]

(joint with Alexandr Zubkov) Quotient sheaves of algebraic supergroups are superschemes, J. Algebra 348 (2011), 135--170; preprint [arXiv1007.2236]

(joint with Pierre Guillot and Christian Kassel) Twisting algebras using non-commutative torsors: explicit computations, Math. Z. 271 (2012), 789--818.

(joint with C. Kassel) Flatness and freeness properties of the generic Hopf Galois extensions, Rev. Un. Mat. Argentina 51 (2010), 79--94.

On minimal quasitriangular pointed Hopf algebras, J. Math. Sci. Univ. Tokyo 16 (2009), 545--576.

(joint with K. Amano and M. Takeuchi) Hopf algebraic approach to Picard-Vessiot theory, Handbook of Algebra Vol. 6, 127--171, Elsevier/North-Holland, Amsterdam, 2009.

Generalized q-boson algebras and their integrable modules, J. Algebra 322 (2009), 2199--2219.

Semisimplicity criteria for irreducible Hopf algebras in positive characteristic. Proc. Amer. Math. Soc. 137 (2009), 1925--1932.

Classifcation of semisimple Hopf algebras, Handbook of Algebra. Vol. 5, 429--455, Elsevier/North-Holland, Amsterdam, 2008.

Construction of quantized enveloping algebras by cocycle deformation, Arab. J. Sci. Eng. Sect. C Theme Issues 33 (2008), 387--406.

Abelian and non-abelian second cohomologies of quantized enveloping algebras, J. Algebra 320 (2008), 1--47.

Formal groups and unipotent affine groups in non-categorical symmetry, J. Algebra 317 (2007), 226--249.

(joint with T. Oka) Unipotent algebraic affine supergroups and nilpotent Lie superalgebras, Algebr. Represent. Theory 8 (2005), 397--413.

The fundamental correspondences in super affine groups and super formal groups, J. Pure Appl. Algebra 202 (2005), 284--312.

(joint with K. Amano) Picard-Vessiot extensions of Artinian simple module algebras, J. Algebra 285 (2005), 743--767.

Example of almost commutative Hopf algebras which are not coquasitriangular, Hopf Algebras, 185--191, Lecture Notes in Pure and Appl. Math. 237, Dekker, New York, 2004.

(joint with C. Calinescu, S. Dascalescu and C. Menini) Quantum lines over non-cocommutative cosemisimple Hopf algebras, J. Algebra 273 (2004), 753--779.

More homological approach to composition of subfactors, J. Math. Sci. Univ. Tokyo 10 (2003), 599--630; available at HP of Graduate School of Math. Sciences, the University of Tokyo.

Hopf cohomology vanishing via approximation by Hochschild cohomology, Noncommutative Geometry and Quantum Groups (Warsaw, 2001), 111--123, Banach Center Publ. 61, Polish Acad. Sci., Warsaw, 2003.

(joint with TadashiYanai) Hopf module duality applied to X-outer Galois theory, J. Algebra 265 (2003), 229--246.

Cohomology and coquasi-bialgebra extensions associated to a matched pair of bialgebras, Adv. Math. 173 (2003), no. 2, 262--315.

Hopf algebra extensions and cohomology, New Directions in Hopf Algebras, 167--209, Math. Sci. Res. Inst. Publ. 43, Cambridge Univ. Press, Cambridge, 2002.

Defending the negated Kaplansky conjecture, Proc. Amer. Math. Soc. 129 (2001), 3185--3192.

Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension, New Trends in Hopf Algebra Theory (La Falda, 1999), 195{214, Contemp. Math. 267, Amer. Math. Soc., Providence, RI, 2000.

Extensions of Hopf algebras and Lie bialgebras, Trans. Amer. Math. Soc. 352 (2000), 3837--3879.

(joint with T. Kobayashi) A result extended from groups to Hopf algebras, Tsukuba J. Math. 21 (1997), 55--58.

Calculations of some groups of Hopf algebra extensions, J. Algebra 191 (1997), 568--588; Corrigendum, J. Algebra 197 (1997), 656.

Faithfully flat forms and cohomology of Hopf algebra extensions, Comm. Algebra 25 (1997), 1169--1197.

Some further classification results on semisimple Hopf algebras, Comm. Algebra 24 (1996), 307--329.

The p^n theorem for semisimple Hopf algebras, Proc. Amer. Math. Soc. 124 (1996), 735--737.

Self-dual Hopf algebras of dimension p^3 obtained by extension, J. Algebra 178 (1995), 791--806.

Semisimple Hopf algebras of dimension 6,8, Israel J. Math. 92 (1995), 361--373.

Semisimple Hopf algebras of dimension 2p, Comm. Algebra 23 (1995), 1931--1940.

(joint with D. Wigner) Faithful flatness of Hopf algebras, J. Algebra 170 (1994), 156--164.

Quotient theory of Hopf algebras, Advances in Hopf Algebras (Chicago, IL, 1992), 107--133, Lecture Notes in Pure and Appl. Math. 158, Dekker, New York, 1994.

Cleft extensions for a Hopf algebra generated by a nearly primitive element, Comm. Algebra 22 (1994), 4537--4559.

Coideal subalgebras in finite Hopf algebras, J. Algebra 163 (1994), 819--831.

(joint with Y. Doi) Generalization of cleft comodule algebras, Comm. Algebra 20 (1992), 3703--3721.

Freeness of Hopf algebras over coideal subalgebras, Comm. Algebra 20 (1992), 1353--1373.

On Hopf algebras with cocommutative coradicals, J. Algebra 144 (1991), 451--466.

Existence of a unique maximal subcoalgebra whose action is inner, Hopf Algebras, Israel J. Math. 72 (1990), 149--157.

Coalgebra actions on Azumaya algebras, Tsukuba J. Math. 14 (1990), 107--112.

Corings and invertible bimodules, Tsukuba J. Math. 13 (1989), 353--362.

Co-Galois theory for field extensions, J. Math. Soc. Japan 41 (1989), 577--592.