Defining relations for classical Lie algebras of polynomial vector fields.
Defining relations for classical Lie superalgebras without Cartan matrices.
Degree one cohomology for the Lie algebras of derivations.
Dérivations et déformations de certaines algèbres de Lie infinies classiques
Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras
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...
Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids.
Dual vector fields ii: calculating the Jacobian
Given a Lie algebra with a chosen basis, the change of coordinates relating coordinates of the first and second kinds near the identity of the corresponding local group yields some remarkable vector fields and dual vector fields. One family of vector fields is dual to a representation of the Lie algebra acting on a Fock-type space. To this representation an abelian family of dual vector fields is associated. The exponential of these commuting operators acting on an appropriate vacuum yields the...