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Modules over the 4-dimensional Sklyanin algebra

Thierry Levasseur; S.Paul Smith — 1993

Bulletin de la Société Mathématique de France

Action du groupe additif

Thierry Levasseur

Groupe d'étude d'algèbre Groupe d'étude d'algèbre

Cohomology of Bimodules Over Enveloping Algebras.

Kenneth A. Brown; Thierry Levasseur — 1985

Mathematische Zeitschrift

Invariant differential operators on the tangent space of some symmetric spaces

Thierry Levasseur; J. Toby Stafford — 1999

Annales de l'institut Fourier

Let $𝔤$ be a complex, semisimple Lie algebra, with an involutive automorphism $ϑ$ and set $𝔨 = Ker (ϑ - I)$ , $𝔭 = Ker (ϑ + I)$ . We consider the differential operators, $𝒟 (𝔭)^{K}$ , on $𝔭$ that are invariant under the action of the adjoint group $K$ of $𝔨$ . Write $τ : 𝔨 \to Der 𝒪 (𝔭)$ for the differential of this action. Then we prove, for the class of symmetric pairs $(𝔤, 𝔨)$ considered by Sekiguchi, that $\{d \in 𝒟 (𝔭) : d (𝒪 (𝔭)^{K}) = 0\} = 𝒟 (𝔭) τ (𝔨)$ . An immediate consequence of this equality is the following result of Sekiguchi: Let $(𝔤_{0}, 𝔨_{0})$ be a real form of one of these symmetric pairs $(𝔤, 𝔨)$ , and suppose that $T$ is a $K_{0}$ -invariant...

Algèbres localement polynomiales

Thierry Levasseur

Groupe d'étude d'algèbre Groupe d'étude d'algèbre

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