Déformations des algèbres de Lie locales et analogue du théorème d'algébricité de Carles.
Deformations of CR-structures on a real Lie-algebra
Sia unalgebra di Lie e (p, J) una sua struttura di Cauchy-Riemann, vale a dire J è una struttura complessa integrabile del sottospazio vettoriale p. Come è stato fatto per il caso delle strutture complesse, cfr. [GT], introduciamo il concetto di deformazione di una struttura CR. Per mezzo dei gruppi di coomologia vengono provati risultati di rigidità. In particolare ogni struttura di Lie- CR che è semisemplice è rigida. Alcuni esempi chiariscono le soluzioni particolari esposte.
Fitting decomposition of Casimir operators of quadratic Lie superalgebras.
Géométrie algébrique de Poisson et déformations
Géométrie de la structure adjointe sur un groupe de Lie et algèbres de type
À partir de l’étude de l’intégrabilité de la structure adjointe sur un groupe de Lie , on est amené à introduire l’algèbre de Lie des opérateurs symétriques du crochet de l’algèbre de Lie de . On fait apparaître une décomposition canonique de toute algèbre de Lie de centre nul en somme directe d’idéaux caractéristiques, où est somme de deux sous-algèbres abéliennes et où est formée d’opérateurs nilpotents.Nous montrons que l’étude de la platitude à l’ordre 2 de la structure adjointe...
Index of Lie algebras of seaweed type.
Indice et polynômes invariants pour certaines algèbres de Lie.
Invariant convex sets and functions in Lie algebras.
Invariant orders in simply connected Lie groups.
Kähler structures and convexity properties of coadjoint orbits.
Leibniz -algebras
A finite-dimensional Lie algebra is called an -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.
Lie algebras
Lie algebras all of whose subalgebras are supersolvable.
A Lie algebra L is said to be minimal non supersolvable if all its subalgebras, except L itself, are supersolvable.
Lie algebras and coverings.
Lie algebras with a given lattice of ideals.
We give a complete classification of Lie Algebras whose lattice of ideals has the length ≤ 2.
Lie Semialgebras are Real Phenomena.
Lie semialgebras in reductive Lie algebras.
Local geometry of orbits for an ordinary classical lie supergroup
In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.
Locally coalescent classes of Lie algebras
Lorentzian Cones in Real Lie Algebras.