Related papers: Commutation Formulae With Respect to Non-Symmetric…
The n-th order covariant derivative on a smooth manifold with an affine connection is a differential operator which turns a function into a tensor field of type (0,n). In this paper the properties of this operatior related to the…
It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
We show that the covariant derivative of a spinor for a general affine connection, not restricted to be metric compatible, is given by the Fock-Ivanenko coefficients with the antisymmetric part of the Lorentz connection. The projective…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained…
The invariants of the Thomas and the Weyl type for a mapping between non-symmetric affine connection spaces are obtained with respect to the factored deformation tensor in this paper. Motivated by two invariants of the Weyl type obtained in…
The simplest i.e. the Abelian i.e. the commutative i.e. the integrable i.e. the flat and torsion-free i.e. the symmetric teleparallel affine connection has been considered in many recent works in the literature. Such an affine connection is…
We give a sufficient condition for a non-commutative association scheme to have a fusion association scheme, and construct non-commutative association schemes from symmetric balanced generalized weighing matrices and generalized Hadamard…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
We make an attempt to develop "noncommutative algebraic geometry" in which noncommutative affine schemes are in one-to-one correspondence with associative algebras. In the first part we discuss various aspects of smoothness in affine…
All possible 1-parametric classical and transcendent degenerated solutions of the fourth Painleve equation with the corresponding connection formulae of the asymptotic parameters are described.
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
This paper presents a non-commutative generalization of the Pfaffian which we call a quasi-Pfaffian. This novel concept arises from solving linear systems with non-commutative skew-symmetric coefficients. A new non-commutative integrable…
A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…
Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…