Mathematische Zeitschrift

, Volume 270, Issue 1, pp 559–575

A remark on the C2-cofiniteness condition on vertex algebras


DOI: 10.1007/s00209-010-0812-4

Cite this article as:
Arakawa, T. Math. Z. (2012) 270: 559. doi:10.1007/s00209-010-0812-4


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 

Copyright information

© 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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