Uniform product of Ag,n(V) for an orbifold model V and G-twisted Zhu algebra
Uniform product of Ag,n(V) for an orbifold model V and G-twisted Zhu algebra
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DOI：
10.1016/j.jalgebra.2003.11.017
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发表时间：
2001-12
影响因子：
0.9
通讯作者：
M. Miyamoto;K. Tanabe
中科院分区：
文献类型：
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作者：
M. Miyamoto;K. Tanabe
让V是一个顶点算子代数和为每个G G有限自同构群诉∈G和非负有理数n∈Z / | G |一个关联代数Ag)、n (V)扮演着一个重要的角色在顶点算子代数理论,但鉴于Ag)产品,n (V)取决于我们表明,G的特征空间。如果V没有负权值有一个统一的定义产品V和我们介绍G-twisted朱代数Ag)、n (V)涵盖所有Ag)、n (V)。设V是一个没有负权的简单顶点算子代数，设S是一个在G作用下闭合的等价不可约扭曲V模的有限集。对于一个合适的由G作用于S的2-环，存在一个有限维的半简单结合代数a α（G， S）。作为AG，n(V)理论的应用，我们证明了一个Schur-Weyl型对偶定理适用于a α（G， S）和VGon的作用（S中扭曲V模的直接和）。这个结果的一个自然结论是：对于任意g∈g，每一个不可约的g-扭转v模都是一个完全可约的v模。
Let V be a vertex operator algebra and G a finite automorphism group of V. For each g∈G and nonnegative rational number n∈ Z /|g| , an associative algebra Ag,n(V) plays an important role in the theory of vertex operator algebras, but the given product in Ag,n(V) depends on the eigenspaces of g. We show that if V has no negative weights then there is a uniform definition of products on V and we introduce a G-twisted Zhu algebra AG,n(V) which covers all Ag,n(V). Let V be a simple vertex operator algebra with no negative weights and let S be a finite set of inequivalent irreducible twisted V-modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra Aα(G, S ) for a suitable 2-cocycle naturally determined by the G-action on S . We show that a duality theorem of Schur–Weyl type holds for the actions of Aα(G, S ) and VGon the direct sum of twisted V-modules in S as an application of the theory of AG,n(V). It follows as a natural consequence of the result that for any g∈G every irreducible g-twisted V-module is a completely reducible VG-module.