The Virasoro group as a complex manifold (Q1902236)

The Virasoro group Vir is a central extension of the group Diff which is the orientation preserving \(C^\infty\) diffeomorphisms of the circle \(s' = R/2 \pi Z\). Both groups Diff and Vir are Lie group models on Fréchet spaces. It does not seem to have been noticed that the group Vir itself carries a natural complex structure -- the present paper is based on this standpoint (cf. Vir admits a left invariant complex structure).