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We continue the work in our earlier paper, ?On certain vertex algebras and their modules associated with vertex algebroids?, J. Algebra 283 (2005), 367?398, to construct and classify graded simple twisted modules for the N-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. In addition, we determine the full automorphism groups of those N-graded vertex algebras in terms of the automorphism groups of the corresponding vertex algebroids.

Twisted modules for vertex algebras associated with vertex algebroids