Communications in Mathematical Physics

, Volume 259, Issue 2, pp 391–411

Abelianizing Vertex Algebras

  • Haisheng Li

DOI: 10.1007/s00220-005-1348-z

Cite this article as:
Li, H. Commun. Math. Phys. (2005) 259: 391. doi: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 decreasing sequence and the sequence Cn introduced by Zhu. By using the (classical) algebra gr(V), we prove that for any vertex algebra V, C2-cofiniteness implies Cn-cofiniteness for all n≥2. We further use gr(V) to study generating subspaces of certain types for lower truncated ℤ-graded vertex algebras.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Haisheng Li
    • 1
    • 2
  1. 1.Department of Mathematical SciencesRutgers UniversityCamdenUSA
  2. 2.Department of MathematicsHarbin Normal UniversityHarbinChina