Abelianizing vertex algebras

TY - JOUR

T1 - Abelianizing vertex algebras

AU - Li, Haisheng

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/24144487068

UR - https://www.scopus.com/pages/publications/24144487068#tab=citedBy

U2 - 10.1007/s00220-005-1348-z

DO - 10.1007/s00220-005-1348-z

M3 - Article

SN - 0010-3616

VL - 259

SP - 391

EP - 411

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -