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ABE Toshiyuki  安部 利之

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ABE Thoshiyuki  安部 利之

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Researcher Number 30380215
Other IDs
Affiliation (Current) 2025: 愛媛大学, 教育学部, 教授
Affiliation (based on the past Project Information) *help 2014 – 2024: 愛媛大学, 教育学部, 教授
2006 – 2013: 愛媛大学, 理工学研究科, 准教授
2010: 愛媛大学, 大学院・理工学研究科, 准教授
2007 – 2008: 愛媛大学, 大学院・理工学研究科, 准教授
2006: Ehime University, Graduate School of Science and Engineering, Lecturer, 大学院理工学研究科, 講師
2005: 愛媛大学, 理学部, 講師
Review Section/Research Field
Principal Investigator
Algebra / Basic Section 11010:Algebra-related
Except Principal Investigator
Algebra
Keywords
Principal Investigator
頂点作用素代数 / オービフォールド模型 / 表現論 / 有限群 / 原田予想 / オービフォールド / ムーンシャイン頂点作用素代数 / 指標 / Moonshine頂点代数 / ツイスト加群 … More / オービオフォールド / 量子次元 / 普遍包絡環 / 誘導表現 / C_2有限性 / 対称群 / C_2 有限性 / コミュタント / 置換オービフォールド / 有限性 / C_2-余有限性 / Virasoro 代数 / 代数学 / 可換環 / 代数 / W-代数 / 共形場理論 … More
Except Principal Investigator
頂点作用素代数 / デザイン / 共形場理論 / 格子 / 散在型単純群 / 単純群 / グラフ / 符号 / 有限群 / 3互換群 / Riemann surface / Lie algebra / Morita equivalence / finite-dimensional algebra / conformal field theory / universal enveloping algebra / vertex operator algebra / トリプレット代数 / ポアソン代数 / Riemann面 / Lie代数 / 森田同値 / 有限次元代数 / 普遍展開環 / 表現論 / 数理物理 / 代数学 / 代数一般 Less
  • Research Projects

    (10 results)
  • Research Products

    (50 results)
  • Co-Researchers

    (20 People)
  •  頂点作用素代数の有限性に関する未解決問題の解決に向けてPrincipal Investigator

    • Principal Investigator
      安部 利之
    • Project Period (FY)
      2024 – 2026
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11010:Algebra-related
    • Research Institution
      Ehime University
  •  Toward to the affirmative solution of some conjectures on finite groups and vertex operator algebrasPrincipal Investigator

    • Principal Investigator
      Abe Toshiyuki
    • Project Period (FY)
      2019 – 2023
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11010:Algebra-related
    • Research Institution
      Ehime University
  •  Study on induced modules of vertex operator algebrasPrincipal Investigator

    • Principal Investigator
      Abe Toshiyuki
    • Project Period (FY)
      2015 – 2018
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Ehime University
  •  Various aspects of sporadic simple groups

    • Principal Investigator
      KITAZUME MASAAKI
    • Project Period (FY)
      2012 – 2017
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Chiba University
  •  Study on finiteness conditions of orbifold models of vertex operator algebrasPrincipal Investigator

    • Principal Investigator
      ABE Toshiyuki
    • Project Period (FY)
      2011 – 2014
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      Algebra
    • Research Institution
      Ehime University
  •  Study on finiteness properties of vertex operator algebrasPrincipal Investigator

    • Principal Investigator
      ABE Toshiyuki
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      Algebra
    • Research Institution
      Ehime University
  •  Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

    • Principal Investigator
      KITAZUME Masaaki
    • Project Period (FY)
      2007 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Chiba University
  •  New developments in representation theories of vertex operator algebras and their applications

    • Principal Investigator
      MATSUO Atsushi
    • Project Period (FY)
      2007 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      The University of Tokyo
  •  頂点作用素代数及びその表現論に関する研究Principal Investigator

    • Principal Investigator
      安部 利之
    • Project Period (FY)
      2005 – 2007
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      Algebra
    • Research Institution
      Ehime University
  •  Expansion and application of representation theory of vertex operator algebras by means of the universal enveloping algebras.

    • Principal Investigator
      MATSUO Atsushi
    • Project Period (FY)
      2005 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      The University of Tokyo

All 2023 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 Other

All Journal Article Presentation

  • [Journal Article] 原田予想IIの解決に向けて2021

    • Author(s)
      安部利之
    • Journal Title

      数理解析研究所講究録

      Volume: 2189 Pages: 77-86

    • Data Source
      KAKENHI-PROJECT-19K03403
  • [Journal Article] On Zp-orbifold constructions of the Moonshine vertex operator algebra2018

    • Author(s)
      Abe Toshiyuki、Lam Ching Hung、Yamada Hiromichi
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 Issue: 1-2 Pages: 683-697

    • DOI

      10.1007/s00209-017-2036-3

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Journal Article] C_2-Cofiniteness of 2-Cyclic Permutation Orbifold Models2013

    • Author(s)
      Toshiyuki Abe
    • Journal Title

      Communications in Mathematical Physics

      Volume: 317 Issue: 2 Pages: 425-445

    • DOI

      10.1007/s00220-012-1618-5

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Journal Article] Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions2013

    • Author(s)
      Toshiyuki Abe, Yusuke Arike
    • Journal Title

      Journal of Algebra

      Volume: 373 Pages: 39-64

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Journal Article] C2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras2011

    • Author(s)
      安部利之
    • Journal Title

      Communications in Mathematical Physics 303, Issue3

      Pages: 825-844

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Journal Article] C_2-Cofiniteness of the 2-Cycle Permutation Orbifold Models of Minimal Virasoro Vertex Operator Algebras2011

    • Author(s)
      安部利之
    • Journal Title

      Communications in Mathematical Physics

      Volume: 303 Pages: 825-844

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Journal Article] A Z_2 orbifold model of the symplectic fermionic vertex perator superalgebra2007

    • Author(s)
      Toshiyuki Abe
    • Journal Title

      Matheroatische Zeitschrift 255(4)

      Pages: 755-792

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540012
  • [Journal Article] A Z_2-orbifold model of the symplectic fermionic Vertex operator superalgebra2007

    • Author(s)
      安部 利之
    • Journal Title

      Mathematische Zeitschrift 255

      Pages: 755-792

    • Data Source
      KAKENHI-PROJECT-17740019
  • [Journal Article] A Z_2 orbifold model of the symplectic fermionic vertex operator superalgebra2007

    • Author(s)
      T.Abe
    • Journal Title

      Mathematische Zeitschrift 255(4)

      Pages: 755-792

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540012
  • [Journal Article] A Z_2 orbifold model of the symplectic fermionic vertex perator superalgebra2007

    • Author(s)
      Toshiyuki Abe
    • Journal Title

      Mathematische Zeitschrift 255(4)

      Pages: 755-792

    • Data Source
      KAKENHI-PROJECT-17540012
  • [Presentation] 原田予想IIとグラム行列式2023

    • Author(s)
      安部利之
    • Organizer
      日本数学会 2023年度年会
    • Data Source
      KAKENHI-PROJECT-19K03403
  • [Presentation] 原田予想IIの解決に向けて2020

    • Author(s)
      安部 利之
    • Organizer
      RIMS 共同研究(公開型) 有限群論,代数的組合せ論,頂点代数の研究
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K03403
  • [Presentation] On V-internal intertwining opearators2019

    • Author(s)
      安部利之
    • Organizer
      代数的組合せ論と関連する群と代数の研究
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K03403
  • [Presentation] On V-internal intertwining opearators and their properties2019

    • Author(s)
      安部 利之
    • Organizer
      Vertex Operator Algebras and Related Topics
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K03403
  • [Presentation] 原田予想への一考察2018

    • Author(s)
      安部 利之
    • Organizer
      草津群論セミナー
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] Extensions of tensor products of the VOA $V_{{\sqrt 2}A_n}^\sigma $2018

    • Author(s)
      安部 利之
    • Organizer
      RIMS共同研究(公開型)「組合せ論的表現論の諸相」
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] Extensions of tensor products of vertex operator algebras $V_{{\sqrt 2}A_n}^{\widehat{\sigma}} $2018

    • Author(s)
      安部 利之
    • Organizer
      Vertex Operator Algebras and Related Topics
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] Group-like fusion をもつ頂点作用素代数の構成について2017

    • Author(s)
      安部利之
    • Organizer
      日本数学会2017年度年会
    • Place of Presentation
      首都大学東京(東京都・八王子市)
    • Year and Date
      2017-03-25
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] A construction of VOAs having group-like fusion2017

    • Author(s)
      安部利之
    • Organizer
      Finite Groups and Vertex Operator Algebras 2017
    • Place of Presentation
      東京女子大学(東京都・杉並区)
    • Year and Date
      2017-03-21
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] ムーンシャイン頂点作用素代数の Zp-軌道体構成について2017

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] The Leech lattice VOA as an extension of V_{√2 A_4}^{\otimes 6}2016

    • Author(s)
      安部利之
    • Organizer
      第33回代数的組合せ論シンポジウム
    • Place of Presentation
      滋賀大学(滋賀県・大津市)
    • Year and Date
      2016-06-24
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] Classification of irreducible modules of Z2×Z2-orbifold model of lattice vertex operator algebras2015

    • Author(s)
      安部利之
    • Organizer
      Vertex operator algebra and related topics
    • Place of Presentation
      成都(中国)
    • Year and Date
      2015-09-07
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15K04823
  • [Presentation] A1 型アフィン頂点作用素代数の 4 次巡回置換オービフォールド模型における, あるコミュタントの構造2014

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-27
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] 頂点作用素代数 $Com_{(L_{\widehat{sl}_2}(1,0)^{\otimes 4})^τ}(L_{\widehat{sl}_2}(4,0))$ の既約加群の分類について2014

    • Author(s)
      安部利之
    • Organizer
      有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-12-16
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] A commutant in a cyclic permutation orbifold model of the lattice vertex operator algebra $V_{A_{1}}$ of order 42014

    • Author(s)
      安部 利之
    • Organizer
      有限群とその表現、頂点作用素代数、代数的組合せ論の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] On S_3-permutation orbifold models of lattice VOA of rank one2013

    • Author(s)
      安部 利之
    • Organizer
      Taitung Workshop
    • Place of Presentation
      国立台東大学(台湾)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] Representation of permutation orbifold models2012

    • Author(s)
      安部 利之
    • Organizer
      Conference on Groups, VOAs and Related Structures
    • Place of Presentation
      筑波大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] On C_2-cofiniteness of permutation orbifold models2012

    • Author(s)
      安部 利之
    • Organizer
      Conference On Vertex Operator Algebras and Related Topics
    • Place of Presentation
      上海交通大学(中国)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] Fusion products for the symplectic-fermionic vertex operator superalgebra2012

    • Author(s)
      安部 利之
    • Organizer
      第29回代数的組合せ論シンポジウム
    • Place of Presentation
      弘前大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] Fusion rules for the symplectic fermionic vertex operator superalgebra2011

    • Author(s)
      安部 利之
    • Organizer
      Conference on Vertex Operator Algebras, Finite groups and Related topics(招待講演)
    • Place of Presentation
      Academia Sinica, Taiwan
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] 置換オービフォールド模型の C_2 有限性について2011

    • Author(s)
      安部 利之
    • Organizer
      第23回草津有限群論セミナー
    • Place of Presentation
      草津セミナーハウス
    • Data Source
      KAKENHI-PROJECT-23740022
  • [Presentation] On C_2-cofiniteness of 2-cycle permutation orbifold models of the Virasoro VOAs2010

    • Author(s)
      安部利之
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] C_2-cofiniteness of Z_2-permutation orbifold models2010

    • Author(s)
      安部利之
    • Organizer
      Research into Vertex Operator Algebras, Finite Groups and Combinatorics
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2010-12-16
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C2-cofiniteness of 2-cycle permutation orbifold models of the Virasoro VOAs2010

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C2-cofiniteness of Z2-permutation orbifold models2010

    • Author(s)
      安部利之
    • Organizer
      頂点作用素代数,群論,組合せ論
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-16
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C_2-cofiniteness of Z_2-orbifold models of vertex operator algebras2009

    • Author(s)
      安部利之
    • Organizer
      有限群・頂点作用素代数と組合せ論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-06
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C_2-cofinteness of vertex operator algebras2009

    • Author(s)
      安部, 利之
    • Organizer
      Algebras, Groups and Geometries 2009 in Tambara
    • Place of Presentation
      丹原セミナーハウス
    • Year and Date
      2009-08-21
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] 可換頂点代数のオービフォールド模型のC2有限性について2009

    • Author(s)
      安部利之
    • Organizer
      第21回草津セミナー
    • Place of Presentation
      群馬県草津セミナーハウス
    • Year and Date
      2009-08-03
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C2-cofiniteness of Z2-orbifold models of vertex operator algebras2009

    • Author(s)
      安部利之
    • Organizer
      有限群・頂点作用素代数と組合せ論
    • Place of Presentation
      京都大学
    • Year and Date
      2009-01-06
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] 可換頂点代数のZN-オービフォールド模型のC2有限性について2009

    • Author(s)
      安部利之
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] 可換頂点代数のオービフォールド模型のC_<2->有限性について2009

    • Author(s)
      安部, 利之
    • Organizer
      第21回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2009-08-03
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C_2-cofiniteness of Z_2-orbifold models of vertex operator algebras2009

    • Author(s)
      Toshiyuki Abe
    • Organizer
      有限群・頂点作用素代数と組合せ論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-06
    • Data Source
      KAKENHI-PROJECT-19540011
  • [Presentation] 可換頂点代数のZ_n-オービフォールド模型のC_2-有限性について2009

    • Author(s)
      安部, 利之
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On C2-cofinteness of vertex operator algebras,Algebras2009

    • Author(s)
      安部利之
    • Organizer
      Groups and Geometries 2009 in Tambara
    • Place of Presentation
      群馬県東京大学丹原セミナーハウス
    • Year and Date
      2009-08-21
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] On representation theory for the symplectic-fermionic vertex operator superalgebra. Algebras2008

    • Author(s)
      Toshiyuki Abe
    • Organizer
      Groups and Geometries 2008
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-11
    • Data Source
      KAKENHI-PROJECT-19540011
  • [Presentation] On representation theory for the symplectic-fermionic vertex operator superalgebra2008

    • Author(s)
      安部利之
    • Organizer
      Algebras, Groups and Geometries 2008
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-10
    • Data Source
      KAKENHI-PROJECT-20740017
  • [Presentation] Frenkel-Zhu両側加群の一般化2008

    • Author(s)
      安部利之
    • Organizer
      第24回代数的組み合わせ論研究集会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-06-28
    • Data Source
      KAKENHI-PROJECT-19540011
  • [Presentation] Frenkel-Zhu 両側加群の一般化2007

    • Author(s)
      安部 利之
    • Organizer
      第24回代数的組み合わせ論研究集会
    • Place of Presentation
      近畿大学
    • Year and Date
      2007-06-28
    • Data Source
      KAKENHI-PROJECT-17740019
  • [Presentation] Frenkel-Zhu両加群の一般化2007

    • Author(s)
      安部利之
    • Organizer
      第24回代数的組み合わせ論研究集会
    • Place of Presentation
      近畿大学
    • Year and Date
      2007-06-28
    • Data Source
      KAKENHI-PROJECT-19540011
  • [Presentation] C2-cofiniteness and rationality of vertex operator algebras

    • Author(s)
      安部利之
    • Organizer
      Algebras, Groups and Geometries
    • Place of Presentation
      東京大学
    • Year and Date
      2014-06-25 – 2014-06-26
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740022
  • 1.  NAGATOMO Kiyokazu (90172543)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 2.  KITAZUME Masaaki (60204898)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 3.  SAWABE Masato (60346624)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 4.  MUNEMASA Akihiro (50219862)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 5.  HARADA Masaaki (90292408)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 6.  CHIGIRA Naoki (40292073)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 7.  MATSUO Atsushi (20238968)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 8.  荒川 知幸 (40377974)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 9.  NOZAWA Sohei (20092083)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 10.  KOSHITANI Shigeo (30125926)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 11.  SUGIYAMA KenーIchi (90206441)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 12.  ANDO Tetsuya (20184319)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 13.  YAMADA Hiromichi (50134888)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 14.  SHIMAKURA Hiroki (90399791)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 15.  LAM ching hung
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 16.  YMAMADA hiromichi
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 17.  NAKASORA Hiroyuki
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 18.  HORIGUCHI Naoyuki
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 19.  IRIE Yuuki
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 20.  KOBAYASHI Yusuke
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results

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