Extension of the Poincaré symmetry and its field theoretical implementation.
Extensions of hom-Lie algebras in terms of cohomology
We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra by another hom-Lie algebra and discuss the case where has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction...
Factorisations des monoïdes libres, bascules, et algèbres de Lie libres
Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras
In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.
Groupes quantiques
Gruppen von Homotopieklassen von Abbildungen in Produkte von Eilenberg-Maclane-Räumen.
Higher-dimensional algebra. VI: Lie 2-algebras.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Invariant measures and controllability of finite systems on compact manifolds
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Irreducible identities of -algebras.
Isogroups and isosubgroups.
The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santilli?s isotheory. We study the isotopic liftings of groups and subgroups and we also deal with the differences between an isosubgroup and a subgroup of an isogroup. Finally, some links between this isotheory and the standard groups theory, referred to representation and equivalence relations among groups are shown.
Koszul homology and Lie algebras with application to generic forms and points.
Large construction for nonsolvable Lie algebras.
L'ensemble des algèbres de lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimension M ... 9.
Lie brackets and real analyticity in control theory
Lie theory and the Chern–Weil homomorphism
Möbius inversion for the Bruhat ordering on a Weyl group
Old and New on S1(2).
On a lie algebra of polynomials