On finite dimensionality of homology of subalgebras of vector fields

Abstract

We show that finite tensor products of modules of tensor fields are Noetherian modules over any graded Lie subalgebra of finite codimension in the Lie algebra of polynomial vector fields on ${\mathbb{R}}^n$. As a corollary, we prove the conjecture of I.\,M. Gelfand, announced at the ICM in Nice in 1970, on the finite-dimensionality of the continuous cohomology of graded Lie subalgebras of finite codimension in the Lie algebra of formal vector fields $W_n$.

The first version of this paper contains a gap in the proof of Noetherianity. This version suggests a completely different proof of Noetherianity

Cited by in corpus (1)

• Polynomial representations of the Witt Lie algebra