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On indecomposable vertex algebras associated with vertex algebroids
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jalgebra.2020.06.004
Phichet Jitjankarn , Gaywalee Yamskulna

Let $A$ be a finite dimensional unital commutative associative algebra and let $B$ be a finite dimensional vertex $A$-algebroid such that its Levi factor is isomorphic to $sl_2$. Under suitable conditions, we construct an indecomposable non-simple $\mathbb{N}$-graded vertex algebra $\overline{V_B}$ from the $\mathbb{N}$-graded vertex algebra $V_B$ associated with the vertex $A$-algebroid $B$. We show that this indecomposable non-simple $\mathbb{N}$-graded vertex algebra $\overline{V_B}$ is $C_2$-cofinite and has only two irreducible modules.

中文翻译:

关于与顶点代数相关的不可分解顶点代数

令$A$为有限维单位交换结合代数,令$B$为有限维顶点$A$-algebroid,使得其Levi因子与$sl_2$同构。在合适的条件下,我们从与顶点 $ 关联的 $\mathbb{N}$-graded 顶点代数 $V_B$ 构造一个不可分解的非简单 $\mathbb{N}$-graded 顶点代数 $\overline{V_B}$ A$-代数$B$。我们证明这个不可分解的非简单 $\mathbb{N}$-graded 顶点代数 $\overline{V_B}$ 是 $C_2$-cofinite 并且只有两个不可约模块。
更新日期:2020-10-01
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