The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 1)
The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 1)
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DOI：
10.1016/j.jalgebra.2021.01.038
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发表时间：
2021-02
影响因子：
0.9
通讯作者：
K. Tanabe
中科院分区：
文献类型：
--
作者：
K. Tanabe
设VL是非退化偶格L上的顶点代数，θ是VL由L的− 1-等距诱导的自同构，VL+是VL在θ作用下的不动点子代数.本文对不可约弱VL +-模进行了分类，证明了任何不可约弱VL +-模同构于某个不可约弱VL-模的弱子模或某个不可约θ-扭VL-模的子模。本文（第一部分）证明了当L的秩为1时，每个非零弱VL +-模包含一个非零M（1）+-模，其中M（1）+是Heisenberg顶点算子代数M（1）在θ作用下的不动点子代数.
Let V L be the vertex algebra associated to a non-degenerate even lattice L, θ the automorphism of V L induced from the− 1-isometry of L, and V L+ the fixed point subalgebra of V L under the action of θ. In this series of papers we classify the irreducible weak V L+-modules and show that any irreducible weak V L+-module is isomorphic to a weak submodule of some irreducible weak V L-module or to a submodule of some irreducible θ-twisted V L-module. In this paper (Part 1), we show that when the rank of L is 1, every non-zero weak V L+-module contains a non-zero M (1)+-module, where M (1)+ is the fixed point subalgebra of the Heisenberg vertex operator algebra M (1) under the action of θ.