Abelianizing vertex algebras

نویسنده

  • Haisheng Li
چکیده

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.

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تاریخ انتشار 2008