The authors consider Lie algebras derived from the Lie algebra
of derivations of the algebra
of formal Laurent series: The Lie algebra
itself, the Lie algebra of all differential operators on
and the Lie algebra of differential operators on
. They prove that each of these Lie algebras has an essentially unique nontrivial central extension. Up to now such results were known only for Lie algebras related to the algebra
of Laurent polynomials.