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.

研究了与√<2>倍a、D、E型普通根格L相关的顶点算子代数的结构。2001年，研究了由相互正交共形向量生成的子代数的格顶点算子代数分解为不可约模的直接和问题。当L =√<2A>_1时，求出权值≤2的所有最高权向量。在L=√<2D>_1的情况下，所有的最高权向量都是由某一保形向量的选择决定的。在L =√<2A>_3的情况下，利用Z_8码构造了一类新的顶点算子代数。在L =√<2A>_3的情况下，得到了moonshine模作为某顶点算子代数的模的完全分解。在2002年，研究了3阶自同构的轨道。发现了中心电荷6/5的W_3代数是√<2A>_2型格顶点算子代数轨道的子代数。

项目成果

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)

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

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

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》。

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

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