Second cohomology space of V ect(R) acting on the space of bilinear bidifferential operators, vanishing on sl(۲)

We consider the V ect(R)-module structure on the spaces of bilinear bidierential operatorsacting on the spaces of weighted densities. We compute the second relative cohomologygroup of the Lie algebra V ect(R) with coecients in the space of bilinear bidierentialoperators that act on tensor densities D;;, vanishing on the Lie algebra sl(۲).This work is the simplest generalization of a result by Basdouri et al. [ Second coho-mology space of sl(۲) acting on the space of bilinear bidierential operators], JournalRevista de la Union Matematica Argentina (۲۰۲۰).

کلیدواژه ها:

lie algebra ، binary Differential Operators ، Weighte Densities