Moonshine: The First Quarter Century and Beyond: Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras
Moonshine: The First Quarter Century and Beyond: Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras
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DOI：
10.1017/cbo9780511730054.015
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Matsuo;K. Nagatomo;A. Tsuchiya
中科院分区：
文献类型：
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作者：
A. Matsuo;K. Nagatomo;A. Tsuchiya
引入了拟有限代数的一般概念，拟有限代数是由满足某些性质的齐次子空间上的所有具有拓扑的整数的集合所分次的代数。引入了正则双模的一个类似物，并描述了拟有限代数上的各种模范畴。当应用到当前代数（通用包络代数）的顶点算子代数满足朱的C2-有限性条件，我们的一般考虑得出的重要后果表示理论的顶点算子代数。特别地，这种顶点算子代数上的模的范畴被证明是等价于有限维结合代数上的模的范畴。
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced and various module categories over quasi-finite algebras are described. When applied to the current algebras (universal enveloping algebras) of vertex operator algebras satisfying Zhu’s C2-finiteness condition, our general consideration derives important consequences on representation theory of such vertex operator algebras. In particular, the category of modules over such a vertex operator algebra is shown to be equivalent to the category of modules over a finite-dimensional associative algebra.