Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI
n-Cohomology of simple highest weight modules on walls and purity.
Nichtsymmetrische sechsdimensionale Liesche Gruppen.
Non-overlapping control systems on Lie groups.
Old and New on S1(2).
On closedness and simple connectedness of adjoint and coadjoint orbits.
On Lie algebra decompositions, related to spherical homogeneous spaces.
On Lie algebroid actions and morphisms
On minimal parabolic subgroups of exponential Lie groups.
On Ol'shanskii's semigroup.
On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups
On some cohomological properties of the Lie algebra of Euclidean motions
The external derivative on differential manifolds inspires graded operators on complexes of spaces , , stated by dual to a Lie algebra . Cohomological properties of these operators are studied in the case of the Lie algebra of the Lie group of Euclidean motions.
On the basic algebraic operations in solvable Lie groups.
On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.
On the equivalence of control systems on Lie groups
We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.
Primitive Ideals and Orbital Integrals in Complex Classical Groups.
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish...
Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.
We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo,...
Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»
Regular orbital measures on Lie algebras
Let H₀ be a regular element of an irreducible Lie algebra , and let be the orbital measure supported on . We show that if and only if k > dim /(dim - rank ).