Study on finiteness properties of vertex operator algebras

• Project/Area Number: 20740017
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Ehime University
• Principal Investigator: ABE Toshiyuki Ehime University, 理工学研究科, 准教授 (30380215)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 頂点作用素代数 / 代数 / オービフォールド / 可換環 / 代数学

Research Abstract

I have been working on a finiteness property called a C_2-cofiniteness property, for a vertex operator algebras. A fixed point subalgebra of a vertex operator algebra by its finite automorphism group is called an orbifold model. In the representation theory of vertex operator algebra there is a conjecture that if a vertex operator algebra has the C_2-cofiniteness property then so does any orbifold model of it. I have found necessary and sufficient conditions which make the conjecture true for commutative vertex algebras and Z_2-permutation orbifold models of vertex operator algebras. I also showed that Z_2-permutation orbifold models of the Virasoro vertex operator algebras having C_2-cofinittness property satisfy the C_2-cofiniteness condition.

Research Products

• [Journal Article] C2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras (2011)
  • Author(s): 安部利之
  • Journal Title: Communications in Mathematical Physics 303, Issue3 Pages: 825-844
  • Peer Reviewed
• [Journal Article] C_2-Cofiniteness of the 2-Cycle Permutation Orbifold Models of Minimal Virasoro Vertex Operator Algebras (2011)
  • Author(s): 安部利之
  • Journal Title: Communications in Mathematical Physics Volume: 303 Pages: 825-844
  • Peer Reviewed
• [Presentation] On C2-cofiniteness of Z2-permutation orbifold models (2010)
  • 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
• [Presentation] C_2-cofiniteness of Z_2-permutation orbifold models (2010)
  • 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
• [Presentation] On C2-cofiniteness of 2-cycle permutation orbifold models of the Virasoro VOAs (2010)
  • 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
• [Presentation] On C_2-cofiniteness of 2-cycle permutation orbifold models of the Virasoro VOAs (2010)
  • 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
• [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
• [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
• [Presentation] On C2-cofinteness of vertex operator algebras,Algebras (2009)
  • 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
• [Presentation] On C_2-cofinteness of vertex operator algebras (2009)
  • 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
• [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
• [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
• [Presentation] On C2-cofiniteness of Z2-orbifold models of vertex operator algebras (2009)
  • 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
• [Presentation] On C_2-cofiniteness of Z_2-orbifold models of vertex operator algebras (2009)
  • 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
• [Presentation] On representation theory for the symplectic-fermionic vertex operator superalgebra (2008)
  • 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