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Abelianizing Vertex Algebras

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Abstract

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, C2-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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rutgers University, Camden, NJ, 08102, USA

    Haisheng Li

  2. Department of Mathematics, Harbin Normal University, Harbin, China

    Haisheng Li

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  1. Haisheng Li
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Communicated by Y. Kawahigashi

Partially supported by an NSA grant

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Li, H. Abelianizing Vertex Algebras. Commun. Math. Phys. 259, 391–411 (2005). https://doi.org/10.1007/s00220-005-1348-z

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  • DOI: https://doi.org/10.1007/s00220-005-1348-z

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