Faculty of Education
数学教育
日本語
Update date：2024/12/27
Professor
Abe Toshiyuki

Research History

  1. 2004/06-2007/03Ehime universityFaculty of ScienceSenior Assistant Professor
  2. 2007/04-2014/03Ehime universityGraduate school of Science and EngineeringAssociate Professor
  3. 2014/04-presentEhime universityFaculty of EducationProfessor

Education

  1. Osaka university1993/041997/03
  2. Osaka university1997/041999/04
  3. Osaka university1999/042002/03

Degree

  1. Doctor of ScienceOsaka University

Research Areas

  1. vertex operator algebra
  2. Japanese Mathematics(Wasan)

Research Interests

  1. representation theory
  2. Lie algebra
  3. group
  4. ring
  5. algebra
  6. vertex operator algebra
  7. conformal field theory
  8. 表現論
  9. リー代数
  10. 群
  11. 環
  12. 代数
  13. 頂点作用素代数
  14. 共形場理論

Research Projects

  1. 頂点作用素代数及びその表現論に関する研究若手研究(B)Principal investigator
  2. Study on finiteness properties of vertex operator algebras若手研究(B)Principal investigator
  3. Study on finiteness conditions of orbifold models of vertex operator algebras若手研究(B)Principal investigator
  4. Study on induced modules of vertex operator algebras基盤研究(C)Principal investigator
  5. 有限群と頂点作用素代数の様々な予想の解決に向けて基盤研究(C)Principal investigator
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Papers

  1. On V-internal intertwining operators2020/09Abe ToshiyukiRIMS Kokyuroku2169(MISC) Prompt report, short report, and research note, etc. (bulletin of university, research institution)
  2. Development and Practice of Teacher Training Program For Improving Leadership of Project Research2019/03Heiwa MUKO Manabu SUMIDA Go NAKAMOTO Takashi KUMAGAI Atsushi OHASHI Yoriko NAKAMURA Masahiro HIZUME Sakae SANO Toshiyuki ABE Naomichi YOSHIMURA Hidenori HAYASHI Yasuyuki YAGI Eiji SATO Yoshihiro YOKOTA Masatsugu MANABE Ryohei OCHI Shinji TANIYAMA大学教育実践ジャーナル17, 55-60Research paper (bulletin of university, research institution)
  3. On Harada conjecture II2019/02Toshiyuki Abe第30回草津群論セミナー(MISC) Summary of the papers read (national conference and other science council)
  4. Extensions of tensor products of Zp-orbifold models of the lattice vertex operator algebra V2Ap−12018/09/15Toshiyuki Abe Ching Hung Lam Hiromichi YamadaJournal of Algebra510, 24-51Research paper (scientific journal)10.1016/j.jalgebra.2018.04.036Academic Press Inc.Let p be an odd prime and let σˆ be an order p automorphism of V2Ap−1 which is a lift of a p-cycle in the Weyl group Weyl(Ap−1)≅Sp. We study a certain extension V of a tensor product of finitely many copies of the orbifold model V2Ap−1 〈σˆ〉 and give a criterion for V that every irreducible V-module is a simple current.
  5. On Zp-orbifold constructions of the Moonshine vertex operator algebra2018/01/13Toshiyuki Abe Ching Hung Lam Hiromichi YamadaMathematische Zeitschrift290/ 1-2, 1-15Research paper (scientific journal)10.1007/s00209-017-2036-3Springer Berlin HeidelbergFor (Formula presented.), we consider a (Formula presented.)-orbifold construction of the Moonshine vertex operator algebra (Formula presented.). We show that the vertex operator algebra obtained by the (Formula presented.)-orbifold construction on the Leech lattice vertex operator algebra (Formula presented.) and a lift of a fixed-point-free isometry of order p is isomorphic to the Moonshine vertex operator algebra (Formula presented.). We also describe the relationship between those (Formula presented.)-orbifold constructions and the (Formula presented.)-orbifold construction in a uniform manner. In Appendix, we give a characterization of the Moonshine vertex operator algebra (Formula presented.) by the existence of an orthogonal pair of Ising vectors.
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Presentations

  1. On Harada conjecture IIRIMS Workshop Research on finite groups, algebraic combinatorics, and vertex algebras2020Oral presentation(invited, special)
  2. On V-internal intertwining operatorsResearch on algebraic combinatorics, related groups and algebras2019/12/17Oral presentation(invited, special)
  3. On V-internal intertwining opearators and their propertiesVertex Operator Algebras and Related Topics2019/08/22Oral presentation(invited, special)
  4. Extensions of tensor products of vertex operator algebras $V_{ { \sqrt 2}A_n}^{\widehat{\sigma } } $Vertex operator algebras and related topics2018/11/04Oral presentation(invited, special)
  5. Extensions of tensor products of the VOA $V_{ { \sqrt 2}A_n}^\sigma $Aspects of Combinatorial Representaion Theory2018/10/12Oral presentation(general)
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Allotted Class

  1. 2024Freshman Seminar B
  2. 2024Linear AlgebraⅠ
  3. 2024Linear Algebra
  4. 2024Teaching Materials: Theoretical Perspectives (Algebra)
  5. 2024Introduction to Mathematics
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Social Activities

  1. 愛媛県高等学校教育研究大会講師2020/12/21
  2. 松山市教科サマーセミナー2020/08/24
  3. えひめサイエンススキルアッププログラム講師2020/07/11-present
  4. Lecturer of certificate renewal couse for teacher2020/07/04-2020/07/04
  5. Lecturer of certificate renewal couse for teacher2019/08/05
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Professional Memberships

  1. Mathematical Society of Japan
  2. 日本数学会
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Committee Memberships

  1. 2015/03-2016/02日本数学会地方地区代議員
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