L'algèbre de Lie des gradients itérés d'un générateur markovien---développements de moyennes et entropies
Le complexe de Koszul en algèbre et topologie
The Koszul complex, as introduced in 1950, was a differential graded algebra which modelled a principal fibre bundle. Since then it has been an effective tool, both in algebra and in topology, for the calculation of homological and homotopical invariants. After a partial summary of these results we recall more recent generalizations of this complex, and some applications.
Left-right noncommutative Poisson algebras
The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as...
Les modules simples sphériques d'une algèbre de Lie nilpotente
L'homologie cyclique des algèbres enveloppantes.
Lie algebra cohomology and generating functions.
Lie Algebra Homology and the Macdonald-kac Formulas.
Lie algebras of least cohomology.
Lie bialgebras real cohomology.
Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
For any Lie-Rinehart algebra , B(atalin)-V(ilkovisky) algebra structures on the exterior -algebra correspond bijectively to right -module structures on ; likewise, generators for the Gerstenhaber algebra correspond bijectively to right -connections on . When is projective as an -module, given a B-V algebra structure on , the homology of the B-V algebra coincides with the homology of with coefficients in with reference to the right -module structure determined by . When...
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure. II