Subalgebras of lattice vertex operator algebras

格点算子代数的子代数

• 批准号: 13640012
• 负责人: YAMADA Hiromichi
• 金额: $ 0.9万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640012/
• 关键词: vertex operator algebra; Virasoro algebra; conformal vector; highest weight vector; moonshine module; orbifold

The structure of vertex operator algebra associated with a lattice L which is √<2> times an ordinary root lattice of type A, D, or E was studied. In 2001, the decomposition of the lattice vertex operator algebra into a direct sum of irreducible modules for a subalgebra generated by mutually orthogonal conformal vectors was studied.1. In the case L = √<2A>_1, all highest weight vectors of weight at most 2 are determined.2. In the case L= √<2D>_1, all highest weight vectors are determined for a certain choice of conformal vectors.3. Using the case L = √<2A>_3, a new type of vertex operator algebras are constructed from Z_8 codes.4. A complete decomposition of the moonshine module as a module for a certain vertex operator algebra related to the case L = √<2A>_3 is obtained.In 2002, the orbifold for an automorphism of order 3 was studied.5. The W_3 algebra of central charge 6/5 is discovered as a subalgebra of the orbifold of the lattice vertex operator algebra of type √<2A>_2.

与晶格L相关的顶点算子代数的结构是√2> <<2>乘以A型，D或E型的普通根晶格。在2001年，晶格顶点操作员代数的分解为由相互正交的共形矢量产生的亚代词的直接总和进行了研究。1。在l =√<2a> _1的情况下，确定了所有最高权重向量2。在l =√<2d> _1的情况下，确定所有最高权重向量针对共同点的一定选择。3。使用情况L =√<2a> _3，由Z_8代码构建了一种新型的顶点操作员代数4。获得月光模块作为与情况L =√<2a> _3相关的特定顶点操作员代数的模块的完整分解。中央电荷的W_3代数6/5被发现为晶格顶点操作员代数的Orbifold的子代数。

项目成果

M. Kitazume, C. H. Lam, H. Yamada: "A class of vertex operator algebras constructed from Z_8 code"Journal of Algebra. 242. 338-359 (2001)

M. Kitazume、C. H. Lam、H. Yamada：“由 Z_8 代码构造的一类顶点算子代数”《代数杂志》。

H.Yamada: "Highest weight vectors with small weights in the vertex operator algebra associated with a lattice of type √2A_1"Communications in Algebra. 29. 1311-1324 (2001)

H.Yamada：“与 √2A_1 类型的格相关的顶点算子代数中具有较小权重的最高权重向量”通讯代数 29. 1311-1324 (2001)

H.Yamada: "Highest weight vectors with small weights in the vertex operator algebra associated with a lattice of type √2 A_1"Communications in Algebra. 29. 1311-1324 (2001)

H.Yamada：“与 √2 A_1 类型的格相关的顶点算子代数中具有较小权重的最高权重向量”通讯代数 29. 1311-1324 (2001)

M.Kitazume, C.H.Lam, H.Yamada: "Moonshine vertex operator algebra as L(1/2,0)×L(7/10)×L(4/5,0)-modules"Journal of Pure and Applied Algebra. 173. 15-48 (2002)

M.Kitazume、C.H.Lam、H.Yamada：“Moonshine 顶点算子代数为 L(1/2,0)×L(7/10)×L(4/5,0)-模”纯粹与应用代数杂志. 173. 15-48 (2002)

H. Yamada: "Highest weight vectors in the vertex operator algebra associated with a lattice of type √<2D>_1"Communications in Algebra. 30. 5065-5089 (2002)

H. Yamada：“与 √<2D>_1 类型的格相关的顶点算子代数中的最高权向量”通讯代数 30. 5065-5089 (2002)