Mathematische Zeitschrift

, Volume 270, Issue 1–2, pp 559–575 | Cite as

A remark on the C2-cofiniteness condition on vertex algebras



We show that a finitely strongly generated, non-negatively graded vertex algebra is C2-cofinite if and only if it is lisse in the sense of Beilinson et al. (preprint). This shows that the C2-cofiniteness is indeed a natural finiteness condition.


Vertex algebras C2-cofiniteness 

Mathematics Subject Classification (2000)

17B69 17B65 17B68 


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsNara Women’s UniversityNaraJapan
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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