Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelianizing vertex algebras   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.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat