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We show that a finitely strongly generated, non-negatively graded vertex algebra $V$ is $C_2$-cofinite if and only if it is lisse in the sense of Beilinson, Feigin and Mazur.
Infinite-dimensional Lie algebras, and the Dedekind η \eta -function
V. G. Kac · 1974
Earlier work this paper cites.
The restriction of admissible representations to 𝔫 {\mathfrak{n}}
William Casselman and M. Scott Osborne · 1978
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Verma modules over the Virasoro algebra
B. L. Feĭgin and D. B. Fuchs · 1984
Earlier work this paper cites.
Vertex algebras, Kac-Moody algebras, and the Monster
Richard E. Borcherds · 1986
Earlier work this paper cites.
Infinite-dimensional Lie algebras
Victor G. Kac · 1990
Earlier work this paper cites.
Rationality of Virasoro vertex operator algebras
Weiqiang Wang · 1993
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Modular invariance of characters of vertex operator algebras
Yongchang Zhu · 1996
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Vertex algebras for beginners
Victor Kac · 1998
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Some finiteness properties of regular vertex operator algebras
Haisheng Li · 1999
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Vertex algebras generated by Lie algebras
Mirko Primc · 1999
Cited alongside, same era.
Modular-invariance of trace functions in orbifold theory and generalized Moonshine
Chongying Dong, Haisheng Li, and Geoffrey Mason · 2000
Cited alongside, same era.
Vertex Lie algebras, vertex Poisson algebras and vertex algebras
Chongying Dong, Haisheng Li, and Geoffrey Mason · 2002
Cited alongside, same era.
Rationality, quasirationality and finite W W -algebras
Matthias R. Gaberdiel and Andrew Neitzke · 2003
Cited alongside, same era.
Chiral algebras
Alexander Beilinson and Vladimir Drinfeld · 2004
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Vertex algebras and algebraic curves
Edward Frenkel and David Ben-Zvi · 2004
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Abelianizing vertex algebras
Haisheng Li · 2005
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Conformal field theories associated to regular chiral vertex operator algebras. I. Theories over the projective line
Kiyokazu Nagatomo and Akihiro Tsuchiya · 2005
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Integrability of C 2 C_{2} -cofinite vertex operator algebras
Chongying Dong and Geoffrey Mason · 2006
Later among the works it cites.
Finite vs affine W W -algebras
Alberto De Sole and Victor G. Kac · 2006
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On simplicity of vacuum modules
Maria Gorelik and Victor Kac · 2007
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Rigidity and modularity of vertex tensor categories
Yi-Zhi Huang · 2008
Later among the works it cites.
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Haisheng Li · 2004
Cited alongside, same era.
Modular invariance of vertex operator algebras satisfying C 2 C_{2} -cofiniteness
Masahiko Miyamoto · 2004
Cited alongside, same era.
Freely generated vertex algebras and non-linear Lie conformal algebras
Alberto De Sole and Victor G. Kac · 2005
Cited alongside, same era.
Associated varieties of modules over Kac-Moody algebras and C 2 C_{2} -cofiniteness of W W -algebras
T. Arakawa
Cited in the paper.
Introduction to algebraic field theory on curves
A. Beilinson, B. Feigin, and B Mazur
Cited in the paper.
Vertex operator algebras and the Verlinde conjecture
Yi-Zhi Huang · 2008
Later among the works it cites.
On rationality of W W -algebras
Victor G. Kac and Minoru Wakimoto · 2008
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Jet schemes and singularities
Lawrence Ein and Mircea Mustaţă · 2009
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