We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

Analogous to the characterisation of Brownian motion on a Riemannian manifold as development Euclidean space, we construct sub-Riemannian diffusions equinilpotentisable manifolds by developing canonical stochastic process arising lift an associated model space. The notion introduce for uses Cartan connections, which take place Levi-Civita connection in geometry. We first derive general expressi...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

After a brief reminder of the Cartan 1-form and its application to the mechanics of point particles we review the application of Cartan 4-forms to eld theory.

We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

We introduce a quasitriangular Hopf algebra or ‘quantum group’ U(B), the double-bosonisation, associated to every braided group B in the category of Hmodules over a quasitriangular Hopf algebra H, such that B appears as the ‘positive root space’, H as the ‘Cartan subalgebra’ and the dual braided group B∗ as the ‘negative root space’ of U(B). The choice B = f recovers Lusztig’s construction of U...

Distributional sources of cosmic walls crossed by cosmic strings from Riemann-Cartan (RC) Geometry. The matter density of the planar wall is maximum at the point where the cosmic string crosses the cosmic wall. Cartan torsion is has a support on the cosmic string given by the Dirac δ-function. Off the sources are left with a torsionless vacuum. PACS number(s) : 0420,0450,1127 Departamento de F́ı...