Cohomology theory of the Virasoro algebra (Q1078651)

The cohomology of the Lie algebra of polynomial vector fields on the circle is studied with coefficients in modules of the form \(u_ iv_ j=(a+bi-j)v_{i+j}\), \(a,b\in \mathbb R\). These modules occur in the Ramond-Neveu-Schwarz superalgebras [see \textit{I. Kaplansky}, Commun. Math. Phys. 86, 49--54 (1982; Zbl 0515.17007)]. It is proved that the mentioned cohomology for \(a\not\in\mathbb Z\) is trivial.