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arXiv · 1908.10446

On Indecomposable Vertex Algebras associated with Vertex Algebroids

Phichet Jitjankarn·Gaywalee Yamskulna
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Abstract

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.

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BibTeXRIS

Phichet Jitjankarn, Gaywalee Yamskulna. 2019-08-27. On Indecomposable Vertex Algebras associated with Vertex Algebroids. https://arxiv.org/abs/1908.10446

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