# On generators and relations for higher level Zhu algebras and applications

@inproceedings{Addabbo2021OnGA, title={On generators and relations for higher level Zhu algebras and applications}, author={Darlayne Addabbo and Katrina Deane Barron}, year={2021} }

Abstract. We give some general results about the generators and relations for the higher level Zhu algebras for a vertex operator algebra. In particular, for any element u in a vertex operator algebra V , such that u has weight greater than or equal to −n for n ∈ N, we prove a recursion relation in the nth level Zhu algebra An(V ) and give a closed formula for this relation. We use this and other properties of An(V ) to reduce the modes of u that appear in the generators for An(V ) as long as u…

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