En utilisant la méthode du double quantique, nous construisons une -matrice universelle pour la quantification de la superalgèbre de Lie . Nous utilisons ce résultat pour construire un invariant d’entrelacs et nous montrons qu’il est égal à une spécialisation du polynôme de Dubrovnik introduit par Kauffman.
A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.
In a JBW*-triple, i.e., a symmetric complex Banach space possessing a predual, the set of tripotents is naturally endowed with a partial order relation. This work is mainly concerned with this partial order relation when restricted to the subset 𝓡(A) of tripotents in a JBW*-triple B formed by the range tripotents of the elements of a JB*-subtriple A of B. The aim is to present recent developments obtained for the poset 𝓡(A) of the range tripotents relative to A, whilst also providing the necessary...
We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. ...
We study the Zariski closures of orbits of representations of quivers of type , ou . With the help of Lusztig’s canonical base, we characterize the rationally smooth orbit closures and prove in particular that orbit closures are smooth if and only if they are rationally smooth.
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in . Some explicit computations of the loop product and the string bracket are given.