Abelianizing vertex algebras

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32 Scopus citations


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 languageEnglish (US)
Pages (from-to)391-411
Number of pages21
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Oct 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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