Sur les algèbres de Lie quasi-filiformes admettant un tore de dérivations

Résumé  Dans ce travail on décrit les algèbres de Lie quasi-filiformes de rang non nul. De plus, on rappelle et corrige la classification des algèbres de Lie filiformes admettant un tore de dérivations, ainsi que la liste des algèbres graduées naturellement et quasi-filiformes.      

Sur certains idéaux d’une algèbre simple

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg -     

Advertible complétude et structure deQ-algèbre

We give different characterizations of algebra types (Q-property, advertible completeness, MackeyQ-property) in terms of the relation ρ<-β and sequentiality notions in locally pseudo-convex algebras.

     

Distances entre exponentielles et puissances d’éléments de certaines algèbres de Banach

Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and let . We show that if then . We also show, assuming a suitable spectral condition on x, that if , then Received: 12 July 2006 Revised: 31 January 2007     

Intégrales orbitales semi-simples et centre de l'algèbre enveloppante

In a previous Note, the first author has established an explicit local formula for semi-simple orbital integrals associated with the Casimir. In this Note, we extend the formula to all elements of the center of the Lie algebra.     

Minima, pentes et algèbre tensorielle

Slopes of an adelic vector bundle exhibit a behaviour akin to successive minima. Comparisons between the two amount to a Siegel lemma. Here we use Zhang’s version for absolute minima over the algebraic numbers. We prove a Minkowski-Hlawka theorem in this context. We also study the tensor product of two hermitian bundles bounding both its absolute minimum and maximal slope, thus improving an estimate of Chen. We further include similar inequalities for exterior and symmetric powers, in terms of some lcm of multinomial coefficients.     

Sur quelques théorémés d’algébre

Annali di Matematica Pura ed Applicata (1858-1865) -     

Analogues non-commutatifs et quasi-symétriques des fonctions de Hall-Littlewood,et modules de Demazure d'une algèbre enveloppante quantique dégénérée

We establish Weyl and Demazure character formulae for certain degenerate quantum groups which admit quasi-symmetric functions as characters. We obtain in this way a new action of the Hecke Algebra on polynomials. This allows us to define quasi-symmetric and non-commutative analogues of Hall-Littlewood functions.     

Sur l'algébre enveloppante d'une algébre de Lie nilpotente

Sans résumé     

Systèmes récursifs et algèbre de hadamard de suites récurrentes linéaires sur des anneaux commutatifs.

Abstract

Let 𝒢 be a simple finite dimensional Lie algebra over the complex numbers and let 𝒢¯ = 𝒢₁ ⊕…⊕ 𝒢 _k be a regular semisimple subalgebra of 𝒢 with each 𝒢 _i being a simple algebra of type A or C. It is shown that the lattice of submodules of a generalized Verma 𝒢-module constructed by parabolic induction starting from a simple torsion free 𝒢¯-module is almost always isomorphic to the lattice of submodules of an associated module formed as a quotient of a classical Verma module by a sum of Verma submodules. In particular, it is shown that the Mathieu admissible Verma modules involved have maximal submodules which are the sum of Verma modules.     

Sur l'algèbre enveloppante d'une algèbre pré-Lie

We construct an associative product on the symmetric module $S(L)$ of any pre-Lie algebra L. It turns $S(L)$ into a Hopf algebra which is isomorphic to the envelopping algebra of $L_{\mathrm{Lie}}$. Then we prove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees. To cite this article: J.-M. Oudom, D. Guin, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Dérivations des Algèbres de Weyl Quantiques Multiparamétrées et de Certaines de leurs Localisations Simples

ABSTRACT

On calcule une base explicite de l'espace des dérivations modulo les dérivations intérieures des algèbres de Weyl quantiques et de certaines de leurs localisations simples. On applique les résultats obtenus à des questions de séparation à équivalence de Morita près de ces algèbres.

We compute an explicit basis of the space of derivations modulo inner derivations for quantum Weyl algebras and some of their simple localizations. We apply these results to separate these algebras up to Morita equivalence.

     

Le degré de similarité d'une algèbre d'opérateurs

Let H be a Hilbert space and let A ⊂B(H) be a unital closed subalgebra (not necessarily self adjoint). We introduce the “degree of similarity” of A, denoted by d(A), which is a non-negative integer or possibly ∞, and we study its significance in connection with the notions of amenability for groups and operator algebras.     

Critère d’existence d’idempotent basé sur les algèbres de Rétrocroisement

We study the relationship of backcrossing algebras with mutation algebras and algebras satisfying ω-polynomial identities: we show that in a backcrossing algebra every element of weight 1 generates a mutation algebra and that for any polynomial identity f there is a backcrossing algebra satisfying f. We give a criterion for the existence of idempotent in the case of baric algebras satisfying a nonhomogeneous polynomial identity and containing a backcrossing subalgebra. We give numerous genetic interpretations of the algebraic results.     

Représentation de Weil associée à une représentation d'une algèbre de Jordan

In the present Note we construct the Weil representation of the Kantor-Koecher-Tits Lie algebra g associated to a simple real Jordan algebra V. Afterwards we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformai group of a Jordan algebra V. We apply this result to the case conformal group SL(2r, ℝ).