Models of quadratic algebras generated by superintegrable systems in 2D.
Models of representations of some classical supergroups.
Octonionic Cayley spinors and
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group , and of its subgroups. We are therefore led to a description of in terms of octonionic matrices, generalizing previous results in the case. Our treatment naturally includes a description of several important subgroups of , notably , , and (the double cover of) . An interpretation of the actions...
On a matched pair of Lie groups for the -Poincaré in 2-dimensions.
On invariants of continuous subgroups of the generalized Poincaré group .
On nets of local algebras on , covariant with respect to the discrete Poincaré group ; causality and scattering theory
On parametrization of the linear and unitary groups in terms of Dirac matrices.
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 contraction of the discrete series of
It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group can be obtained via contraction from the discrete series of representations of .
On the minimal canonical realizations of the Lie algebra
On the polarizers of compact semi-simple Lie groups. Applications
On the supergroup and its superfield representations
On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
Parallélismes absolus des variétés lorentziennes
Tout parallélisme absolu d’une variété lorentzienne complète et simplement connexe respecte une décomposition de de Rham ; dans le cas faiblement irréductible mais non irréductible, la variété est un groupe de Lie résoluble.
Partial Differential Operators and Discrete Subgroups of a Lie Group.
Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations
Polarization and Unitary Representations of Solvable Lie Groups.
Proposition de structures géométriques «amplifiées» pour le traitement des systèmes de points matériels
Quantification géométrique : théorie et exemples
Quantization of pencils with a gl-type Poisson center and braided geometry
We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...