Algebra gl(λ) Inside the Algebra of Differential Operators on the Real Line

Abstract

The Lie algebra gl(λ) with λ ∈ ℂ, introduced by B L Feigin, can be embedded into the Lie algebra of differential operators on the real line (see [7]). We give an explicit formula of the embedding of gl(λ) into the algebra of differential operators on the space of tensor densities of degree λ on ℝ. Our main tool is the notion of projectively equivariant symbol of a differential operator.