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Central extensions of some Lie algebras


Authors: Wanglai Li and Robert L. Wilson
Journal: Proc. Amer. Math. Soc. 126 (1998), 2569-2577
MSC (1991): Primary 17B65, 17B56; Secondary 17B66.
DOI: https://doi.org/10.1090/S0002-9939-98-04348-2
MathSciNet review: 1451817
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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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Additional Information

Wanglai Li
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: wli@math.rutgers.edu

Robert L. Wilson
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: rwilson@math.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04348-2
Keywords: Lie algebra, central extension, 2-cocycle
Received by editor(s): September 13, 1996
Received by editor(s) in revised form: February 4, 1997
Additional Notes: The second author was supported in part by NSF Grant DMS-9401851
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society

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