Abelianizing vertex algebras
نویسنده
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.
منابع مشابه
Vertex Lie algebras, vertex Poisson algebras and vertex algebras
The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.
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