Le groupe de Poincaré et ses représentations. II. (algèbre de Lie, algèbre enveloppante)
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs...
Les sous-algèbres de Cartan réelles et la frontière d'une orbite ouverte dansune variété de drapeaux.
Lie Algebra Cohomology and the Resolution of Certain Harish-Chandra Modules.
Lie algebra structure in the model of 3-link snake robot
In this paper, we study a 5 dimensional configuration space of a 3-link snake robot model moving in a plane. We will derive two vector fields generating a distribution which represents a space of the robot’s allowable movement directions. An arbitrary choice of such generators generates the entire tangent space of the configuration space, i.e. the distribution is bracket-generating, but our choice additionally generates a finite dimensional Lie algebra over real numbers. This allows us to extend...
Lie algebras of a class of top spaces.
Liftings of linear vector fields to product preserving gauge bundle functors on vector bundles.
Loop group decompositions in the generalized method.
Lorentzian Cones in Real Lie Algebras.