Central extensions of some Lie algebras

Li, Wanglai; Wilson, Robert

doi:10.1090/S0002-9939-98-04348-2

Central extensions of some Lie algebras
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by Wanglai Li and Robert L. Wilson

Proc. Amer. Math. Soc. 126 (1998), 2569-2577

DOI: https://doi.org/10.1090/S0002-9939-98-04348-2

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Abstract:

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

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