Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras

Abstract

In this paper, all one-dimensional Leibniz central extensions on the algebras of differential operators over Ct, t ^?1] and C((t)), as well as on the quantum 2-torus, the Virasoro-like algebra and its q-analog are studied. We determine all nontrivial Leibniz 2-cocycles on these infinite dimensional Lie algebras.