This paper analyses non-regular |2|-graded geometries, and show that they share many of the properties of regular geometries – the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as obstruction to flatness of the geometry, the existence of the first two BGG splitting operators and of (in most cases) invariant prolongations for the standard Tractor b...

Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space S = UOSp(1|2)/U(1). We analyze the superspace geometry of the supersphere, in particular deriving the invariant vielbein and spin connection from a generalization of the left-invariant Maurer-Cartan form for Lie groups. Using this information we pr...

Model of Riemann–Cartan gravity with varying signature metric is considered. The basic dynamical variables the formalism are vierbein, spin connection, and an internal in tangent space. corresponding action contains new terms, which depend on these fields. In general case determined dynamically. Minkowski preferred dynamically because configurations other signatures suppressed. We also discuss ...

When performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian met...

Cartan subalgebras, automorphisms and the UCT problem Selçuk Barlak This talk deals with the connection between the UCT problem for separable, nuclear C*-algebras and Cartan subalgebras, that is, MASAs that admit faithful conditional expectations and whose normalizers generate the ambient C*-algebras. We present a characterization, in terms of Cartan subalgebras, of the UCT for fixed point alge...

The goal of this paper is to express the Bach tensor of a four– dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach t...

Asking that the metric of a complex Finsler space should be strong convex, Abate and Patrizio ([1]) associate to the real tangent bundle a real Finsler metric for which they analyze the relation between Cartan (real) connection of the obtained space and the real image of Chern-Finsler complex connection. Following the same ideas, in the present paper we shall deal with the more general case of ...

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold. To accomplish this, we introduce and investigate the notions of semispray and nonlinear connection associated with a given regular connection, in the pullb...

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...

Abstract We present a framework for the computation of Hopf 2-cocycles involved in deformations Nichols algebras over semisimple algebras. write down recurrence formula and investigate extent connection with invariant Hochschild cohomology terms exponentials. As an example, we detailed computations leading to explicit description algebra Cartan type $A_2$ $q=-1$ , a.k.a. positive part small qua...