Cette note évoque les premiers travaux de J.-L. Koszul (1947-1950) en les replaçant dans leur cadre historique et retrace en particulier le chemin qui a conduit Koszul à la résolution qui porte son nom.
La première partie de cet article est une adaptation au cadre des super groupes d’un théorème dû à Cartier qui assure que les groupes formels sont lisses en caractéristique zéro. La seconde partie donne une description des super groupes de Lie dits “vraiment classiques” comme groupes d’automorphismes de super algèbres semi-simples associatives à involution, selon une méthode de Weil.
In [6], there is a graphic description of any irreducible, finite dimensional module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional -modules.In the present work, we generalize this construction to . We show it is in fact a description of the reduced shape algebra, a quotient of the shape algebra of . The basis used in [6] is thus naturally parametrized with the so called quasi standard Young tableaux....
In un'algebra di Lie graduata thin, la classe in cui compare il secondo diamante e la caratteristica del campo soggiacente determinano se l'algebra stessa abbia o meno dimensione finita ed in tal caso forniscono anche un limite superiore a tale dimensione.
In this paper the problem of obstructions in Lie algebra deformations is studied from four different points of view. First, we illustrate the method of local ring, an alternative to Gerstenhaber’s method for Lie deformations. We draw parallels between both methods showing that an obstruction class corresponds to a nilpotent local parameter of a versal deformation of the law in the scheme of Jacobi. Then, an elimination process in the global ring, which defines the scheme, allows us to obtain nilpotent...
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...
The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.