According to J. Feldman and C. Moore’s wellknown theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e., a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C∗-algebraic analogue of this theore...

This study conducts the modeling and numerical analysis of a screw dislocation in three-dimensional continuous medium. Our is based on differential geometry Weitzenböck manifold, i.e., Riemann-Cartan manifold which equips itself with non-zero torsion affine connection. Following to standard framework geometrical elasto-plasticity, we introduce three smooth manifolds representing reference R, in...

According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e. a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C *-algebraic analogue of this theor...

We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi-Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex

It is safe to say that the theory of modular representations of finite groups is not a part of the average mathematician's toolkit. Matrix representations of finite groups over the complex field, and the resulting characters (traces of matrices), occur rather widely in both pure and applied mathematics. But replacing complex numbers by elements of a finite or other field of prime characteristic...

In scalar-tensor theories of gravity with torsion, the gravitational field is described in terms of a symmetric metric tensor g, a metriccompatible connection ∇ with torsion, and a scalar field φ. The main aim is to explore an interaction of a charged perfect fluid and a scalar field φ in a background electromagnetic and gravitational field described by {g, ∇, φ}. The interaction is based on an...

Cartan matrices are of fundamental importance in representation theory. For algebras defined by quivers (i.e. directed graphs) with relations the computation of the entries of the Cartan matrix amounts to counting nonzero paths in the quivers, leading naturally to a combinatorial setting. In this paper we study a refined version, so-called q-Cartan matrices, where each nonzero path is weighted ...

between any two coordinates ( i) and ( i). Hence any choice of Γ k ij in one coordinate chart suffices to define the connection in another. Let T k ij := Γkij − Γkji be the torsion tensor of the connection. The case when torsion is zero (torsion-free) is of particular interest in geometry. In Hermann Weyl’s terms [11], the very existence of inertia systems in the Universe warrants that its line...

A rotating universe represented by the Gödel metric in spacetimes with Cartan torsion is investigated where the Cosmic Microwave Background Radiation (CMBR) is computed from the Gödel rotation of the universe and the spin density of the spinning fluid in EinsteinCartan gravity.The autoparallel equation in Riemann-Cartan spacetime is shown to lead to the evolution equation of the cosmological pe...