Orbifolds of vertex operator algebras

顶点算子代数的轨道

• 批准号: 15540015
• 负责人: YAMADA Hiromichi
• 金额: $ 1.41万
• 依托单位: Hitotsubashi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540015/
• 关键词: vertex operator algebra; orbifold; Virasoro algebra; fusion rule; parafermion algebra; W algebra; ムーンシャイン加群

Orbifolds by automorphisms of vertex operator algebras associated with positive definite even lattices were studied and the following results were obtained.(1)Irreducible twisted modules with respect to an automorphism of a lattice vertex operator algebra lifted from a fixed point free isometry of a lattice were classified.(2)A vertex operator algebra associated with √2 times a root lattice of type A_2 was studied. It was shown that the orbifold by a certain automorphism of order 3 possesses an order 3 symmetry. The relation of the symmetry and 3A elements of the monster was discussed.(3)A vertex operator algebra associated with √2 times a root lattice of type A_l for a general rank l was studied. A parafermion algebra was constructed inside the vertex operator algebra.(4)A W_3 algebra of central charge 6/5 was constructed inside an orbifold by an order 3 automorphism of a vertex operator algebra associated with √2 times a root lattice of type A_2. Its irreducible modules were classified also.(5)A vertex operator algebra, which is called a tricritical 3-state Potts model in physics, was constructed inside a vertex operator algebra associated with √2 times a root lattice of type E_6. Moreover, its irreducible modules were classified and the fusion rules were determined.

研究了与正定偶格相关的顶点算子代数自同构的轨道折叠，得到了以下结果。(1)对由定点自由等距提升的点阵顶点算子代数自同构的不可约扭曲模进行了分类。(2)与√2倍根相关的顶点算子代数 研究了A_2型晶格。结果表明，具有一定3阶自同构的轨道折叠具有3阶对称性。讨论了怪物的对称性与3A元的关系。(3)研究了一般秩l的与√2倍A_l型根格相关的顶点算子代数。在顶点算子代数内部构造了对费米子代数。(4)利用与√2倍A_2型根格相关的顶点算子代数的3阶自同构，在轨道折叠内构造了中心电荷6/5的W_3代数。 (5)在与√2倍E_6型根格相关的顶点算子代数内部构造了顶点算子代数，物理学上称为三临界三态Potts模型。并对其不可约模块进行了分类并确定了融合规则。

项目成果

Z_3-twisted representations of lattice vertex operator algebras

格点算子代数的 Z_3 扭曲表示

• 发表时间: 2003
• 期刊: Communications in Algebra 31
• 作者: C.H.Lam;H.Yamada
• 通讯作者: H.Yamada

C.H.Lam, H.Yamada: "Z_3-twisted representations of lattice vertex operator algebras"Commnications in Algebra. 31. 3001-3020 (2003)

C.H.Lam、H.Yamada：“格子顶点算子代数的 Z_3 扭曲表示”代数通讯。

C.H.Lam, H.Yamada: "Decomposilion of the lattice vertex operator algebra V_√2A_1"Journal of Algebra. 272. 614-624 (2004)

C.H.Lam，H.Yamada：“格顶点算子代数 V_√2A_1 的分解”代数杂志 272. 614-624 (2004)

Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes

由三元代码构造的三临界三态 Potts 模型和顶点算子代数

• 发表时间: 2004
• 期刊: Communications in Algebra 32
• 作者: C.H.Lam;H.Yamada
• 通讯作者: H.Yamada

3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group

3 态 Potts 模型、Moonshine 顶点算子代数和 Monster 群的 3A 元素

• 发表时间: 2003
• 期刊: International Mathematical Research Notices 23
• 作者: N.Kitazume;C.H.Lam;H.Yamada
• 通讯作者: H.Yamada