Vertex algebroids and conformal vertex algebras associated with simple Leibniz algebras

We first investigate the algebraic structure of vertex algebroids B when B are simple Leibniz algebras. Next, we use these vertex algebroids B to construct indecomposable non-simple C2-cofinite N-graded vertex algebras VB‾. In addition, we classify N-graded irreducible VB‾-modules and examine conformal vectors of these N-graded vertex algebras VB‾.