Abelianizing vertex algebras

Details Abelianizing vertex algebras Abelianizing vertex algebras

2004-09-08

arxiv.org/abs/math/0409140v1

Mathematics

Quantum Algebra

Latex, 24 pages

Scientific paper

10.1007/s00220-005-1348-z

To every vertex algebra $V$ we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space $gr(V)$ is naturally a vertex Poisson algebra, in particular a commutative vertex algebra. We establish a relation between this sequence and the sequence $C_{n}$ introduced by Zhu. By using the (classical) algebra $gr(V)$, we prove that for any vertex algebra $V$, $C_{2}$-cofiniteness implies $C_{n}$-cofiniteness for all $n\ge 2$. We further use $gr(V)$ to study generating subspaces of certain types for lower truncated $Z$-graded vertex algebras.

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