Research on modules over fixed point vertex subalgebras

• Project/Area Number: 20740002
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: TANABE Kenichiro 北海道大学, 大学院・理学研究院, 准教授 (10334038)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 頂点代数 / 群論 / 頂点作用素代数 / 微分体 / 多元環

Research Abstract

(1)I investigated the finite-dimensional modules over vertex algebras constructed from commutative algebras. I showed that every finite-dimensional module over a fixed point differential subfield has a structure of twisted module over the original differential field.
(2)I generalized a notion of a twisted module over a vertex algebra. Moreover I constructed a corresponding Zhu algebra. Namely, I established a correspondence between the simple generalized twisted modules over a vertex algebra and the simple modules over the Zhu algebra. This correspondence is a natural generalization of the results by Zhu.

Research Products

• [Journal Article] Finite-dimensional vertex algebra moaules over fixed point differential subfields (2012)
  • Author(s): Kenichiro Tanabe
  • Journal Title: J.Algebra Volume: 356 Issue: 1 Pages: 1-16
  • DOI: 10.1016/j.jalgebra.2012.02.001
  • Peer Reviewed
• [Journal Article] Finite-dimensionalvertex algebra modules over fixed pointcommutative subalgebras (2011)
  • Author(s): Kenichiro Tanabe
  • Journal Title: J. Algebra Volume: 337 Issue: 1 Pages: 323-334
  • DOI: 10.1016/j.jalgebra.2011.04.024
  • Peer Reviewed
• [Journal Article] Representations of a fixed pointsubalgebra of a class of lattice vertexoperator algebras by an automorphism oforder three (2009)
  • Author(s): Kenichiro Tanabe and Hiromichi Yamada
  • Journal Title: European Journal ofCombinatorics Volume: 30 Issue: 3 Pages: 725-735
  • DOI: 10.1016/j.ejc.2008.07.002
• [Journal Article] Representations of a fixed point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three (2009)
  • Author(s): 田邊顕一朗
  • Journal Title: European Journal of Combinatorics 30巻 Pages: 725-735
  • Peer Reviewed
• [Journal Article] Representations of a fixed point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three (2009)
  • Author(s): K. Tanabe and H. Yamada
  • Journal Title: European Journal of Combinatorics 30 Pages: 725-735
  • Peer Reviewed
• [Journal Article] Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra (2008)
  • Author(s): 田邊顕一朗
  • Journal Title: J.Algebra 320巻 Pages: 1261-1274
  • Peer Reviewed
• [Presentation] 頂点代数のtwisted加群について (2012)
  • Author(s): Kenichiro Tanabe
  • Organizer: 有限群と頂点作用素代数
  • Place of Presentation: 東京女子大学(東京都)(招待講演)
  • Year and Date: 2012-02-18
• [Presentation] 頂点代数のツイステッド加群について (2012)
  • Author(s): Kenichiro Tanabe
  • Organizer: 日本数学会年会(2012年)
  • Place of Presentation: 東京理科大学
• [Presentation] 頂点代数のツイステッド加群について、有限群と頂点作用素代数 (2012)
  • Author(s): Kenichiro Tanabe
  • Place of Presentation: 東京女子大学
• [Presentation] On vertex algebramodules over commutative algebras (2010)
  • Author(s): Kenichiro Tanabe
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 河北師範大学(中国)
• [Presentation] 有限群の作用で不変な部分微分体上の頂点代数としての有限次元加群 (2010)
  • Author(s): Kenichiro Tanabe
  • Organizer: 日本数学会年会(2010年)
  • Place of Presentation: 慶應義塾大学矢上キャンパス
• [Presentation] On vertex algebra modules over commutative algebras (2010)
  • Author(s): 田邊顕一朗
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 河北師範大学(中国)
• [Presentation] 有限群の作用で不変な部分微分体上の頂点代数としての有限次元加群 (2010)
  • Author(s): 田邊顕一朗
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶應義塾大学矢上キャンパス
• [Presentation] On modules for vertex algebras constructed from quadratic extensions of the nolvnomial ring in one variable (2009)
  • Author(s): K. Tanabe
  • Organizer: Korea-Japan Workshop on Algebra and Combinatorics
  • Place of Presentation: Pusan National University
  • Year and Date: 2009-02-09
• [Presentation] 一変数多項式環の二次拡大から構成される頂点代数の有限次元加群 (2009)
  • Author(s): Kenichiro Tanabe
  • Place of Presentation: 遊学館(山形県生涯学習センター)
• [Presentation] 可換多元環から構成される頂点代数の加群について (2009)
  • Author(s): Kenichiro Tanabe
  • Organizer: 日本数学会年会(2009年)
  • Place of Presentation: 東京大学駒場キャンパス
• [Presentation] On modules for vertexalgebras constructed from quadraticextensions of the polynomial ring in onevariable (2009)
  • Author(s): Kenichiro Tanabe
  • Organizer: Korea-Japan Workshop on Algebraand Combinatorics
  • Place of Presentation: Pusan National University
• [Presentation] 一変数多項式環の二次拡大から構成される頂点代数の有限次元加群 (2009)
  • Author(s): 田邊顕一朗
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 遊学館(山形県生涯学習センター)
• [Presentation] 可換多元環から構成される頂点代数の加群について (2009)
  • Author(s): 田邊顕一朗
  • Organizer: 日本数学会2009年度年会
  • Place of Presentation: 東京大学駒場キャンパス
• [Presentation] On modules for vertex algebras constructed from quadratic extensions of the polynomial ring in one variable (2009)
  • Author(s): 田邊顕一朗
  • Organizer: Korea-Japan Workshop on Algebra and Combinatorics
  • Place of Presentation: Pusan National University (韓国)