Related papers: Linear connections on matrix geometries
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space equal to the projectivization of the noncommutative symmetric algebra of a k-central two -sided…
Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph $G=(V,…
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…
We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and non degenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
For a simplicial manifold we construct the differential geometry structure and use it to investigate linear connections, metric and gravity. We discuss and compare three main approaches and calculate the resulting gravity action…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…