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R -matrice universelle pour U h ( D ( 2 , 1 , x ) ) et invariant d’entrelacs associé

Henrik Thys (2002)

Bulletin de la Société Mathématique de France

En utilisant la méthode du double quantique, nous construisons une R -matrice universelle pour la quantification de la superalgèbre de Lie D ( 2 , 1 , x ) . 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.

Rational smoothness of varieties of representations for quivers of Dynkin type

Philippe Caldero, Ralf Schiffler (2004)

Annales de l’institut Fourier

We study the Zariski closures of orbits of representations of quivers of type A , D ou E . 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.

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

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 M . We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C * ( M ) with coefficients in C * ( M ) . Some explicit computations of the loop product and the string bracket are given.

Reductive homogeneous spaces and nonassociative algebras

Alberto Elduque (2020)

Communications in Mathematics

The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.

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