Researcher Database

ABE, Toshiyuki

FacultyFaculty of Education Mathematics Education
PositionProfessor
Last Updated :2019/07/11

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

その他基本情報

Association Memberships

  • Mathematical Society of Japan

Committee Memberships

  • 2015/03 -2016/02

Academic & Professional Experience

  • 2014/04 - Today, Professor, Ehime university
  • 2007/04 - 2014/03, Associate Professor, Ehime university
  • 2004/06 - 2007/03, Lecturer, Ehime university

Research Activities

Research Areas, Etc.

Research Areas

  • Mathematics, Algebra, vertex operator algebra

Research Interests

  • vertex operator algebra
  • representation theory
  • group
  • Lie algebra
  • conformal field theory
  • ring
  • 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, 17, 55, 60, 2019/03
  • 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, 510, 24, 51, 2018/08, 10.1016/j.jalgebra.2018.04.036
  • On ${\mathbb {Z}}_p$-orbifold constructions of the Moonshine vertex operator algebra, ABE Toshiyuki, Mathematische Zeitschrift, 290, 1-2, 683, 697, 2018/01, 10.1007/s00209-017-2036-3
  • Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions, Toshiyuki Abe, Yusuke Arike, Yusuke Arike, Journal of Algebra, 373, 39, 64, 2013/01, 00218693, 10.1016/j.jalgebra.2012.09.022
  • $C_2$-cofiniteness of 2-cyclic permutation orbifold models, Toshiyuki Abe, Communications in Mathematical Physics, 317, 425, 445, 2013/01, 00103616, 10.1007/s00220-012-1618-5
  • $C_2$-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras, Toshiyuki Abe, Communications in Mathematical Physics, 303, 825, 844, 2011/05, 00103616, 10.1007/s00220-011-1209-x
  • A ${\mathbb Z}_2$ -orbifold model of the symplectic fermionic vertex operator superalgebra, Toshiyuki Abe, Mathematische Zeitschrift, 255, 755, 792, 2007/04, 00255874, 10.1007/s00209-006-0048-5
  • Rationality of the vertex operator algebra $V_L^+$ for a positive definite even lattice $L$, Toshiyuki Abe, Mathematische Zeitschrift, 249, 455, 484, 2005/02, 00255874, 10.1007/s00209-004-0709-1
  • Fusion rules for the vertex operator algebras $M(1)^+$ and $V_L^+$, Toshiyuki Abe, Chongying Dong, Haisheng Li, Haisheng Li, Communications in Mathematical Physics, 253, 171, 219, 2005/01, 00103616, 10.1007/s00220-004-1132-5
  • Rationality, regularity, and $C_2$-cofiniteness, Toshiyuki Abe, Toshiyuki Abe, Geoffrey Buhl, Geoffrey Buhl, Chongying Dong, Transactions of the American Mathematical Society, 356, 3391, 3402, 2004/08, 00029947, 10.1090/S0002-9947-03-03413-5
  • Classification of irreducible modules for the vertex operator algebra $V_L^+$: General case, Toshiyuki Abe, Chongying Dong, Journal of Algebra, 273, 657, 685, 2004/03, 00218693, 10.1016/j.jalgebra.2003.09.043
  • Finiteness of conformal blocks over compact Riemann surfaces, Toshiyuki Abe, Toshiyuki Abe, Kiyokazu Nagatomo, Osaka Journal of Mathematics, 40, 375, 391, 2003/06, 00306126
  • Finiteness of conformal blocks over the projective line, ABE Toshiyuki, Fields Institute Communications, 39, 1, 12, 2003
  • The charge conjugation orbifold $V_{{\mathbb Z}\alpha}^+$ is rational when $\langle\alpha,\alpha\rangle/2$ is prime, Toshiyuki Abe, International Mathematics Research Notices, 647, 665, 2002/09, 10737928
  • Fusion rules for the charge conjugation orbifold, ABE Toshiyuki, Journal of Algebra, 242, 2, 624, 655, 2001/08, 10.1006/jabr.2001.8838
  • Fusion rules for the free bosonic orbifold vertex operator algebra, ABE Toshiyuki, Journal of Algebra, 229, 1, 333, 374, 2000/07

Conference Activities & Talks

Misc

  • 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 $\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(4,0)$ in the cyclic permutation orbifold model $(\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(1,0)^{\otimes 4})^\tau$ with $\tau=(1\,2\,3\,4)$. It is shown that the commutant is isomorphic to a ${\mathbb Z}_2\times{\mathbb Z}_2$-orbifold model of a tensor product of two lattice type vertex operator algebras of rank one.
  • 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, 18802818, http://ci.nii.ac.jp/naid/110008667175
  • 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) among simple modules for the vertex operator algebra obtained as an even part of the symplectic fermionic vertex operator superalgebra. By using these fusion rules we show that the fusion algebra of this vertex operator algebra is isomorphic to the group algebra of the Klein four group over Z.
  • 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, 18802818, http://ci.nii.ac.jp/naid/110007130761
  • 1476, 182, 187, 2006/03, 18802818, 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 to a finite dimensional vector space with a nondegenerate skew-symmetric bilinear form. We also classify its equivalence classes of irreducible modules 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 even lattice $L$ has an automorphism of order 2 lifted from -1-isometry of $L$. We prove that for the fixed point vertex operator algebra $V_L^+$, any $\Z_{\geq0}$-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 Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general condition, for instance, $C_2$-finiteness, we prove that conformal blocks are of finite dimensional. This, in particular, shows the finiteness of conformal blocks for many well-known conformal field theories including WZNW 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 $<\alpha,\alpha>/2$ 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 $V_L^+$ 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 operator algebra are completely determined.

Other Research Activities

Research Grants & Projects

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