On indecomposable vertex algebras associated with vertex algebroids

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 sl2. Under suitable conditions, we construct an indecomposable non-simple N-graded vertex algebra VB‾ from the N-graded vertex algebra VB associated with the vertex A-algebroid B. We show that this indecomposable non-simple N-graded vertex algebra VB‾ is C2-cofinite and has only two irreducible modules.