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 decreasing 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 ≥ 2. We further use gr(V) to study generating subspaces of certain types for lower truncated ℤ-graded vertex algebras.
|Original language||English (US)|
|Number of pages||21|
|Journal||Communications In Mathematical Physics|
|State||Published - Oct 2005|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics