## Serge Skryabin

## Degree one cohomology for the Lie algebras of derivations

## (Lobachevskii Journal of Mathematics, Vol.14, pp.85-123)

Let $R$ be a commutative ring and $W$ a Lie algebra of its derivations which is an
$R$-submodule in the full derivation algebra
$\Der R$. We consider a class of
$W\!$-modules generalizing the natural
representations of the Lie algebras of vector
fields in tensor fields of arbitrary type. The
main result consists in the determination of the
cohomology of those modules in degree 1. Its
applications include a description of derivations
and the universal central extension for the Lie
algebra $W$.

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