ABE Toshiyuki

J-GLOBAL         Last updated: Jul 10, 2019 at 14:50
 
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Name
ABE Toshiyuki
Affiliation
Ehime University
Section
Faculty of Education
Job title
Professor
Degree
Doctor of Science(Osaka University)
Research funding number
30380215

Research Areas

 
 
  • Mathematics / Algebra / vertex operator algebra

Academic & Professional Experience

 
Apr 2014
 - 
Today
Professor, Faculty of Education, Ehime university
 
Apr 2007
 - 
Mar 2014
Associate Professor, Graduate school of Science and Engineering, Ehime university
 
Jun 2004
 - 
Mar 2007
Lecturer, Faculty of Science, Ehime university
 

Education

 
Apr 1999
 - 
Mar 2002
Mathematics, Graduate school of Science Doctor course, Osaka university
 
Apr 1997
 - 
Apr 1999
Mathematics, Graduate school of Science Master course, Osaka university
 
Apr 1993
 - 
Mar 1997
Mathematics, Faculty of Sicence, Osaka university
 

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   Mar 2019   [Refereed]
ABE Toshiyuki
Journal of Algebra   510 24-51   Aug 2018   [Refereed]
ABE Toshiyuki
Mathematische Zeitschrift   290(1-2) 683-697   Jan 2018   [Refereed]
Toshiyuki Abe, Yusuke Arike, Yusuke Arike
Journal of Algebra   373 39-64   Jan 2013
We determine fusion rules (dimensions of the spaces 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 s...
Toshiyuki Abe
Communications in Mathematical Physics   317 425-445   Jan 2013
In this article, we consider permutation orbifold models of Tex-cofinite
vertex operator algebras of CFT type. We show the Tex-cofiniteness of the
2-cyclic permutation orbifold model Tex for an arbitrary
Tex-cofinite simple ...
Toshiyuki Abe
Communications in Mathematical Physics   303 825-844   May 2011   [Refereed]
In this article, we give a sufficient and necessary condition for the
Tex-cofiniteness of the 2-cycle permutation orbifold model Tex for a Tex-cofinite vertex operator algebra and the 2-cycle
permutation Tex of $V\otimes...
Toshiyuki Abe
Mathematische Zeitschrift   255 755-792   Apr 2007   [Refereed]
We give an example of an irrational C 2-cofinite vertex operator algebra whose central charge is -2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex operator superalgebra generated by d pairs of sym...
Toshiyuki Abe
Mathematische Zeitschrift   249 455-484   Feb 2005   [Refereed]
The lattice vertex operator algebra VL associated to a positive definite even lattice L has an automorphism of order 2 lifted from - 1-isometry of L. The fixed point set VL+ of VL for the automorphism is naturally a vertex operator algebra. We pro...
Toshiyuki Abe, Chongying Dong, Haisheng Li, Haisheng Li
Communications in Mathematical Physics   253 171-219   Jan 2005   [Refereed]
The fusion rules for the vertex operator algebras M(1)+ (of any rank) and VL + (for any positive definite even lattice L) are determined completely. © Springer-Verlag 2004.
Toshiyuki Abe, Toshiyuki Abe, Geoffrey Buhl, Geoffrey Buhl, Chongying Dong
Transactions of the American Mathematical Society   356 3391-3402   Aug 2004   [Refereed]
We demonstrate that, for vertex operator algebras of CFT type, C 2-cofiniteness and rationality is equivalent to regularity. For C 2-coflnite vertex operator algebras, we show that irreducible weak modules are ordinary modules and C 2-connite. V L...
Toshiyuki Abe, Chongying Dong
Journal of Algebra   273 657-685   Mar 2004   [Refereed]
The irreducible modules for the fixed point vertex operator subalgebra VL + of the vertex operator algebra VL associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are classified. © 200...
Toshiyuki Abe, Toshiyuki Abe, Kiyokazu Nagatomo
Osaka Journal of Mathematics   40 375-391   Jun 2003   [Refereed]
Finiteness of conformal blocks over the projective line
ABE Toshiyuki
Fields Institute Communications   39 1-12   2003   [Refereed]
Toshiyuki Abe
International Mathematics Research Notices   647-665   Sep 2002   [Refereed]
ABE Toshiyuki
Journal of Algebra   242(2) 624-655   Aug 2001   [Refereed]
Fusion rules for the free bosonic orbifold vertex operator algebra
ABE Toshiyuki
Journal of Algebra   229(1) 333-374   Jul 2000   [Refereed]

Misc

 
Toshiyuki Abe, Hiromichi Yamada
   Apr 2014
We study the commutant of the vertex operator algebra
Tex in the cyclic permutation
orbifold model Tex with Tex. It is shown t...
Toshiyuki Abe, Yusuke Arike
   Aug 2011
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 sh...

Conference Activities & Talks

 
Extensions of tensor products of vertex operator algebras Tex [Invited]
ABE Toshiyuki
Vertex operator algebras and related topics   4 Nov 2018   
Extensions of tensor products of the VOA Tex
ABE Toshiyuki
Aspects of Combinatorial Representaion Theory   12 Oct 2018   
On a construction of VOAs having group-like fusion
ABE Toshiyuki
MSJ Spring Meeting 2017   25 Mar 2017   
A construction of VOAs having group-like fusion, [Invited]
ABE Toshiyuki
Finite Groups and Vertex Operator Algebras 2017   21 Mar 2017   
The Leech lattice VOA as an extension of Tex
ABE Toshiyuki
Jun 2016   
Classification of irreducible modules of Tex-orbifold model of lattice vertex operator algebras
ABE Toshiyuki
Vertex Operator Algebras and Related Topics   7 Sep 2015   
Tex-cofiniteness and rationality of vertex operator algebras
ABE Toshiyuki
Algebras, Groups and Geometries   25 Jun 2014   
A commutant in a cyclic permutation orbifold model of the lattice vertex operator algebra Tex of order Tex
ABE Toshiyuki
K07A245309H   5 Mar 2014   
On Tex-permutation orbifold models of lattice VOA of rank one
ABE Toshiyuki
Taitung Workshop   26 Mar 2013   
Representation of permutation orbifold models
ABE Toshiyuki
Conference on Groups, VOAs and Related Structures   10 Sep 2012   

Association Memberships

 
 

Research Grants & Projects

 
Toward solutions of vary conjectures in group theory and the theory of vertex operator algebra
Mext: 
Project Year: Apr 2019 - Mar 2021    Investigator(s): Abe, Toshiyuki
Study on induced representations of vertex operator algebras
mext: 
Project Year: Apr 2015 - Mar 2019    Investigator(s): ABE Toshiyuki
Study on finiteness properties of orbifold models of vertex operator algebras
mext: 
Project Year: Apr 2011 - Mar 2015    Investigator(s): ABE Toshiyuki
Study on finiteness properties of vertex operator algebras
mext: 
Project Year: Apr 2008 - Mar 2011    Investigator(s): ABE Toshiyuki
Study on vertex operator algebras and its representation theory
mext: 
Project Year: Apr 2005 - Mar 2008    Investigator(s): ABE Toshiyuki

Social Contribution

 
Lecturer of certificate renewal couse for teacher
[Lecturer]  mext  certificate renewal couse  15 Jul 2018
Lecturer of certificate renewal couse for teacher
[Lecturer]  mext  certificate renewal couse  14 Jul 2017
Lecturer for high school students
[Lecturer]  Ehime university  8 Jun 2017
Lecturer of certificate renewal couse for teacher
[Lecturer]  mext  certificate renewal couse  7 Aug 2016
Lecturer of certificate renewal couse for teacher
[Lecturer]  mext  certificate renewal couse  25 Jul 2015
Lecturer for high school students
[Lecturer]  Ehime university  29 Jan 2014
Lecturer for high school students
[Lecturer]  Ehime university  1 Aug 2013
Lecturer for high school students
[Lecturer]  Ehime university  31 Jul 2013
Lecturer for high school students
[Lecturer]  Ehime university  10 Dec 2012
Lecturer for high school students
[Lecturer]  Ehime university  2 Oct 2012

Others

 
Mar 2017   Workshop VOA and related topics
Sep 2012   Conference on Groups, VOAs and Related Structures in Honor of Masahiko Miyamoto