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

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