A remark on the \(C_2\)-cofiniteness condition on vertex algebras (Q663252)

In the paper under review that author presents an important characterization of \(C_2\)-cofinite vertex algebras. He proves that a finitely strongly generated, non-negatively graded vertex algebra is \(C_2\)-cofinite if and only if it is lisse in the sense of \textit{A. Beilinson}, \textit{B. Feigin} and \textit{B. Mazur} [``Introduction to algebraic field theory on curves'', Preprint]. This equivalence is discussed in the cases of rational affine and Virasoro vertex operator algebras.