Researcher Database

ABE, Toshiyuki

FacultyFaculty of Education Mathematics Education
PositionProfessor
Last Updated :2020/05/28

Researcher Profile and Settings

Profile and Settings

Name

  • Name

    ABE, Toshiyuki

Affiliations

Affiliation & Job

  • Section

    Faculty of Education
  • Job title

    Professor

Education, Etc.

Education

  • 1999/04 - 2002/03, Osaka university, Graduate school of Science Doctor course
  • 1997/04 - 1999/04, Osaka university, Graduate school of Science Master course
  • 1993/04 - 1997/03, Osaka university, Faculty of Sicence

Degree

  • Doctor od Science

その他基本情報

Committee Memberships

  • 2015/03 - 2016/02

Academic & Professional Experience

  • 2014/04 - Today, Professor, Faculty of Education, Ehime university
  • 2007/04 - 2014/03, Associate Professor, Graduate school of Science and Engineering, Ehime university
  • 2004/06 - 2007/03, Lecturer, Faculty of Science, Ehime university

Research Activities

Research Areas, Etc.

Research Areas

  • Natural sciences, Algebra, vertex operator algebra

Book, papers, etc

Published Papers

  • Development and Practice of Teacher Training Program For Improving Leadership of Project Research, Heiwa 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, 2019/03, [Refereed]
  • Extensions of tensor products of ${\mathbb Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1 } }, ABE Toshiyuki, Journal of Algebra, Journal of Algebra, 2018/08, [Refereed], 10.1016/j.jalgebra.2018.04.036
  • On ${\mathbb {Z } }_p$-orbifold constructions of the Moonshine vertex operator algebra, ABE Toshiyuki, Mathematische Zeitschrift, Mathematische Zeitschrift, 2018/01, [Refereed], 10.1007/s00209-017-2036-3
  • 2017
  • $C_2$-cofiniteness of 2-cyclic permutation orbifold models, Toshiyuki Abe, Communications in Mathematical Physics, Communications in Mathematical Physics, 2013/01, [Refereed], 0010-3616, 10.1007/s00220-012-1618-5
  • 2013/01, [Refereed], 0021-8693, 10.1016/j.jalgebra.2012.09.022
  • 2011/05, [Refereed], 0010-3616, 10.1007/s00220-011-1209-x
  • 2007/04, [Refereed], 0025-5874, 10.1007/s00209-006-0048-5
  • 2005/02, [Refereed], 0025-5874, 10.1007/s00209-004-0709-1
  • 2005/01, [Refereed], 0010-3616, 10.1007/s00220-004-1132-5
  • 2004/03, [Refereed], 0021-8693, 10.1016/j.jalgebra.2003.09.043
  • 2004, [Refereed], 0002-9947, 10.1090/S0002-9947-03-03413-5
  • 2003/06, [Refereed], 0030-6126
  • Finiteness of conformal blocks over the projective line, ABE Toshiyuki, Fields Institute Communications, Fields Institute Communications, 2003, [Refereed]
  • 2002, [Refereed], 1073-7928
  • Fusion rules for the charge conjugation orbifold, ABE Toshiyuki, Journal of Algebra, Journal of Algebra, 2001/08, [Refereed], 10.1006/jabr.2001.8838
  • 2000/07, [Refereed], 0021-8693

Conference Activities & Talks

Misc

  • On Harada conjecture II, Toshiyuki Abe, 2019/02
  • 69, 83, 108, 2017/02
  • 1965, 13, 20, 2015/10, 1880-2818, http://ci.nii.ac.jp/naid/110009983696
  • A commutant in a cyclic permutation orbifold model of the lattice vertex operator algebra $V_{A_1}$ of order $4$ (Research on finite groups and their representations, vertex operator algebras, and algebraic combinatorics), Abe Toshiyuki, RIMS Kokyuroku, Kyoto University, RIMS Kokyuroku, 1926, 114, 121, 2014/12, 1880-2818, http://ci.nii.ac.jp/naid/110009871914
  • Commutant of $\mathcal{L}_{\widehat{\mathfrak{sl } }_2}(4,0)$ in the cyclic permutation orbifold of $\mathcal{L}_{\widehat{\mathfrak{sl } }_2}(1,0)^{\otimes 4}$, Toshiyuki Abe, Hiromichi Yamada, 2014/04, http://arxiv.org/abs/1404.1974v1, We study the commutant of the vertex operator algebra<br /> $\mathcal{L}_{\widehat{\mathfrak{sl } }_2}(4,0)$ in the cyclic permutation<br /> orbifold model $(\mathcal{L}_{\widehat{\mathfrak{sl } }_2}(1,0)^{\otimes<br /> 4})^\tau$ with $\tau=(1\,2\,3\,4)$. It is shown that the commutant is<br /> isomorphic to a ${\mathbb Z}_2\times{\mathbb Z}_2$-orbifold model of a tensor<br /> product of two lattice type vertex operator algebras of rank one.
  • Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions, Toshiyuki Abe, Yusuke Arike, 2011/08, http://arxiv.org/abs/1108.1823v1, We determine fusion rules (dimensions of the space of intertwining operators)<br /> among simple modules for the vertex operator algebra obtained as an even part<br /> of the symplectic fermionic vertex operator superalgebra. By using these fusion<br /> rules we show that the fusion algebra of this vertex operator algebra is<br /> isomorphic to the group algebra of the Klein four group over Z.
  • On $C_2$-cofiniteness of $\mathbb{Z}_2$-permutation orbifold models of vertex operator algebras (Research into Vertex Operator Algebras, Finite Groups and Combinatorics), Abe Toshiyuki, RIMS Kokyuroku, Kyoto University, RIMS Kokyuroku, 1756, 94, 100, 2011/08, 1880-2818, http://ci.nii.ac.jp/naid/110008667175
  • On $C_2$-confiniteness of $\mathbb{Z}_2$-orbifold models of vertex operator algebras (Finite Groups, Vertex Operator Algebras and Combinatorics), Abe Toshiyuki, RIMS Kokyuroku, Kyoto University, RIMS Kokyuroku, 1656, 7, 12, 2009/07, 1880-2818, http://ci.nii.ac.jp/naid/110007130761
  • 1476, 182, 187, 2006/03, 1880-2818, http://ci.nii.ac.jp/naid/120000901573
  • A ${\mathbb Z}_2$-orbifold model of the symplectic fermionic vertex operator superalgebra, Toshiyuki Abe, K07A245309H, 2005/03, http://arxiv.org/abs/math/0503472v2, We construct an irrational C_2-cofinite vertex operator algebra associatted<br /> to a finite dimensional vector space with a nondegenerate skew-symmetric<br /> bilinear form. We also classify its equivalence classes of irreducible modules<br /> and determine its automorphism group.
  • Rationality of the vertex operator algebra $V_L^+$ for a positive definite even lattice $L$, Toshiyuki Abe, 2003/11, http://arxiv.org/abs/math/0311210v1, The lattice vertex operator algebra $V_L$ associated to a positive definite<br /> even lattice $L$ has an automorphism of order 2 lifted from -1-isometry of $L$.<br /> We prove that for the fixed point vertex operator algebra $V_L^+$, any<br /> $\Z_{\geq0}$-graded weak modules is completely reducible.
  • Finiteness of conformal blocks over compact Riemann surfaces, Toshiyuki Abe, Kiyokazu Nagatomo, 2002/01, http://arxiv.org/abs/math/0201037v1, We study conformal blocks (the space of correlation functions) over compact<br /> Riemann surfaces associated to vertex operator algebras which are the sum of<br /> highest weight modules for the underlying Virasoro algebra. Under the fairly<br /> general condition, for instance, $C_2$-finiteness, we prove that conformal<br /> blocks are of finite dimensional. This, in particular, shows the finiteness of<br /> conformal blocks for many well-known conformal field theories including WZNW<br /> model and the minimal model.
  • 1228, 76, 80, 2001/09, 1880-2818, http://ci.nii.ac.jp/naid/110000165756
  • 1218, 8, 14, 2001/06, 1880-2818, http://ci.nii.ac.jp/naid/110000165580
  • The charge conjugation orbifold $V_{ { \mathbb Z}\alpha}^{+}$ is rational when $\langle\alpha,\alpha\rangle /2$ is prime, Toshiyuki Abe, K07A245309H, 2001/01, http://arxiv.org/abs/math/0101204v1, We prove that the vertex operator algebra $V_{Z\alpha}^{+}$ is rational if<br /> $&lt;\alpha,\alpha&gt;/2$ is a prime integer.
  • Fusion rules for the charge conjugation orbifold, Toshiyuki Abe, 2000/06, http://arxiv.org/abs/math/0006101v1, We completely determine the fusion rules for the vertex operator algebra<br /> $V_L^+$ for a rank one even lattice $L$.
  • Fusion rules for the free bosonic orbifold vertex operator algebra, Toshiyuki Abe, 1999/07, http://arxiv.org/abs/math/9907120v1, Fusion rules among irreducible modules of the free bosonic orbifold vertex<br /> operator algebra are completely determined.

Other Research Activities

Research Grants & Projects

Others

Activity track record

Educational activities

Course in charge

  • 2019, the first semester, under graduate, 新入生セミナーB
  • 2019, the first semester, under graduate, 線形代数
  • 2019, the first semester, under graduate, 線形代数Ⅰ
  • 2019, the first semester, under graduate, 線形代数Ⅰ
  • 2019, the first semester, under graduate, 数学科教育法Ⅲ
  • 2019, the first semester, under graduate, 数学科教育法3
  • 2019, the first semester, under graduate, 代数学3
  • 2019, the first semester, under graduate, 数学・情報研究
  • 2019, the first semester, under graduate, 数学科教育法3


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