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arXiv · 2211.08510

On finite dimensionality of homology of subalgebras of vector fields

Boris Feigin·Alexei Kanel-Belov·Anton Khoroshkin
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Abstract

We show that the tensor product of modules of tensor fields is a noetherian module as a module 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 ICM'1970 at Nice on finite dimensionality of continuous cohomology of graded Lie subalgebras of formal vector fields $W_n$.

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Boris Feigin, Alexei Kanel-Belov, Anton Khoroshkin. 2022-11-15. On finite dimensionality of homology of subalgebras of vector fields. https://arxiv.org/abs/2211.08510

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