Starting from a real analytic surface ℳ with conformal Cartan connection A. Bor´owka constructed minitwistor space of an asymptotically hyperbolic Einstein–Weyl manifold being the boundary. In this article, starting symmetry connection, we prove that symmetries on can be extended to obtained manifold.

We construct simple twistor–like actions describing superparticles propagating on a coset superspace OSp(1|4)/SO(1, 3) (containing the D = 4 anti–de–Sitter space as a bosonic subspace), on a supergroup manifold OSp(1|4) and, generically, on OSp(1|2n). Making two different contractions of the superparticle model on the OSp(1|4) supermanifold we get massless superparticles in Minkowski superspace...

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibn...

Suppose G is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let G/G denote the orbit space of G and C∗(G) denote the groupoid C∗-algebra. Suppose that G is a principal groupoid. We show that C∗(G) is CCR if and only if G/G is a T1 topological space, and that C∗(G) is GCR if and only if G/G is a T0 topological space. We also show that C∗(G) is a Fell Algeb...

A spinning fluid embedded in a space section flat Friedmann model is used to compute the cosmological density perturbation of the model.The spinning fluid obeys the Einstein-Cartan field equations while the Friedmann embedded model is assumed to obey the general the Friedmann equation in General Relativity.It is shown that at the early epochs of the Universe the spin-torsion contribution to the...

Let G be a real semisimple Lie group. Let g0 be the Lie algebra of G. We will denote the complexification of any vector space V0 by V and its dual by V ∗. Let g0 = k0 + p0 be a fixed Cartan decomposition corresponding to the Cartan involution θ of g0. Let K be the corresponding maximal compact subgroup of G. Let us fix T ⊂ K a maximal torus. Define S ⊂ t∗ as the set of weights of T that are sum...

We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in...

The Cartan subalgebra of the quantum loop algebra Uq(Lsl2) is generated by a family of mutually commuting operators, responsible for the l-weight decomposition of finite dimensional Uq(Lsl2)-modules. The natural Jordan filtration induced by these operators is generically non-trivial on l-weight spaces of dimension greater than one. We derive, for every standard module of Uq(Lsl2), the dimension...

In the study of submanifolds in a homogeneous space X = G/P of a Lie group G, the method of moving frames is both a unifying concept and an effective tool, which is the version of the method of equivalence applied to submanifold geometry. Let φ be the left invariant, Lie algebra g-valued Maurer-Cartan form of G. The local equivalence problem for a submanifold f : M →֒ X is solved on a canonical ...

The chains studied in this paper generalize Chern–Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of different types). The aim of this paper is to study the relation between these...