ABE Toshiyuki 安部利之

… Alternative Names

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

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

[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

ABE Toshiyuki 安部 利之

ABE Thoshiyuki 安部 利之

Research Projects

Research Products

Co-Researchers

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

Project Period (FY)

Research Category

Review Section

Research Institution

Toward to the affirmative solution of some conjectures on finite groups and vertex operator algebrasPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Study on induced modules of vertex operator algebrasPrincipal Investigator

Principal Investigator

Project Period (FY)

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Various aspects of sporadic simple groups

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Study on finiteness conditions of orbifold models of vertex operator algebrasPrincipal Investigator

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Study on finiteness properties of vertex operator algebrasPrincipal Investigator

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Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

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New developments in representation theories of vertex operator algebras and their applications

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頂点作用素代数及びその表現論に関する研究Principal Investigator

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Expansion and application of representation theory of vertex operator algebras by means of the universal enveloping algebras.

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[Journal Article] 原田予想IIの解決に向けて2021

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[Journal Article] On Zp-orbifold constructions of the Moonshine vertex operator algebra2018

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[Journal Article] C_2-Cofiniteness of 2-Cyclic Permutation Orbifold Models2013

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[Journal Article] Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions2013

ABE Toshiyuki 安部利之

ABE Thoshiyuki 安部利之