Abstract
We consider three Lie algebras: D e r C ( ( t ) ) Der \mathbb {C}((t)) , the Lie algebra of all derivations on the algebra C ( ( t ) ) \mathbb {C}((t)) of formal Laurent series; the Lie algebra of all differential operators on C ( ( t ) ) \mathbb {C}((t)) ; and the Lie algebra of all differential operators on C ( ( t ) ) ⊗ C n . \mathbb {C}((t))\otimes \mathbb {C}^n. We prove that each of these Lie algebras has an essentially unique nontrivial central extension.
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