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Central extensions of some Lie algebras. (English) Zbl 0916.17017
The authors consider Lie algebras derived from the Lie algebra Der((t)) of derivations of the algebra ((t)) of formal Laurent series: The Lie algebra Der((t)) itself, the Lie algebra of all differential operators on ((t)) and the Lie algebra of differential operators on ((t)) n . 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 [t,t -1 ] of Laurent polynomials.

MSC:
17B56Cohomology of Lie (super)algebras
17B65Infinite-dimensional Lie (super)algebras
17B66Lie algebras of vector fields and related (super)algebras