Harish-Chandra pairs and affine algebraic group schemes in the Verlinde category, revisited, submitted, available on request.
(joint with Kensuke Egami and Kenta Suzuki) Smoothness of commutative Hopf algebras, Comm. Algebra, published online: DOI: 1080/00927872.2025.2557373
(joint with Yuta Takahashi) Quotients in super-symmetry: formal supergroup case, Comm. Algebra 52 (2024) no.10, 4075–4092; DOI: 10.1080/00927872.2024.2338492
Supersymmetric Picard-Vessiot theorey, preprint [arXiv2307.01997]
(joint with Takuya Oe, Yuta Takahashi) Torsors in super-symmetry, J. Noncom. Geometry (2025), 19 (2025), no.3, 931–969. DOI10.4171/JNCG/603; 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; https://doi.org/10.5802/afst.1665
(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; DOI:10.4171/JNCG/237; preprint [arXiv1404.4941]; DOI 10.4171/JNCG/237
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; available at HP of Graduate School of Math. Sciences, the University of Tokyo
(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; https://doi.org/101016/j.jalgebra.2009.03.019
Semisimplicity criteria for irreducible Hopf algebras in positive characteristic. Proc. Amer. Math. Soc. 137 (2009), 1925--1932; https://doi.org/10.1090/S0002-9939-09-09863-3
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; https://doi.org/10.1016/j,jalgebra.2008.03.034
Formal groups and unipotent affine groups in non-categorical symmetry, J. Algebra 317 (2007), 226--249; https://doi.org/10.1016/j.jalgebra.2007.03.006
(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; https://doi.org/10.1016/j.jpaa.2005.02.010
(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; DOI: 10.4064/bc61-0-8
(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; https://doi.org/10.1090/S0002-9947-00-02394-1
(joint with T. Kobayashi) A result extended from groups to Hopf algebras, Tsukuba J. Math. 21 (1997), 55--58; available at Tsukuba Repository
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; https://doi.org/10.101006/jabr.1994.1332
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; https://doi.org/10.101006/0021-8693(91)90116-P
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; available at Tsukuba Repository
Corings and invertible bimodules, Tsukuba J. Math. 13 (1989), 353--362; available at Tsukuba Repository
Co-Galois theory for field extensions, J. Math. Soc. Japan 41 (1989), 577--592; https://doi.org/10.2969/jmsj/0414577