Research on structural symmetries of vertex operator algebras
| Project/Area Number |
16K05073
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 頂点作用素代数 / ヴィラソロ代数 / ３互換群 / テンソル圏 / 双対性 / 三互換群 / グライス代数 / 単純カレント / 散在型有限単純群 / 共形デザイン |
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| Outline of Final Research Achievements |
I have researched on structural symmetries of vertex operator algebras of OZ-type. The Griess algebra is a finite dimensional substructure of a vertex operator algebra which is an infinite dimensional object. I have proved the uniqueness of the structure of a simple vertex operator algebra generated by Ising vectors of sigma-type, where the Griess algebra for such a vertex operator algebra is described by Matsuo algebras. I have also researched on a vertex operator algebras which involves a subalgebra having group-like fusion. I have described a duality between Grothendieck rings of the representation categories of vertex operator overalgebra/subalgebra via quadratic forms on finite abelian groups arising from modular tensor category.
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| Academic Significance and Societal Importance of the Research Achievements |
高い対称性を持った構造は数学および物理学で重要であり，また興味を引く研究対象である。本研究では二次元共形場理論の代数的定式化である頂点作用素代数における対称性について，構造論によるアプローチで研究を行い，３互換群に関連するクラスについて，内在的な特徴付けを与える成果を得た。また，このようなクラスに属する例を与える構成法について一般論を展開し，フュージョン代数間の双対性を有限可換群上の二次形式による双対性として記述する理論を確立した。
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Report
(4 results)
Research Products
(14 results)
