Lie Subalgebras of Differential Operators in One Variable

Abstract

[EN] Let Witt be the Lie algebra generated by the set {Li |i ∈ Z} and Vir its universal central extension. Let Diff(V ) be the Lie algebra of differential operators on V = C((z)), C[[z]] or V = C(z). We explicitly describe all Lie algebra homomorphisms from sl(2), Witt, and Vir to Diff(V ), such that L0 acts on V as a first-order differential operator.