Related papers: Noncommutative Cross-Ratios
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
We introduce the notion of a cross-frame potential function, which takes one frame as input and returns its cross-frame potential value with respect to another frame. We analyze the behavior of this new function to determine what…
We establish the ultra-violet finiteness of various classes of noncommutative gauge theories.
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
We give equivalences between given properties of a commutative ring, and other properties on its ring of Witt vectors. Amongst them, we characterise all commutative rings whose rings of Witt vectors are Noetherian. We define a new category…
In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of…
In 1702.04949 noncommutative frames were introduced, generalizing the usual notion of frames of open sets of a topological space. In this paper we extend this notion to noncommutative Grothendieck topologies and their associated…
This note is an introductory survey of non-Hausdorff separation axioms. The main focus is to study properties that are between $T_0$ and $T_1$, properties between $T_1$ and Hausdorff and how the $T_0$-quotient change them and the relation…
We introduce the new notion of epsilon-graded associative algebras which takes its root into the notion of commutation factors introduced in the context of Lie algebras. We define and study the associated notion of epsilon-derivation-based…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
We provide the necessary and sufficient condition for a pointwise slant submanifold with respect to two anti-commuting almost Hermitian structures to be also pointwise slant with respect to a family of almost Hermitian structures generated…
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
The relation between symmetry breaking in non-commutative cut-off field theories and transitions to inhomogeneous phases in condensed matter is discussed. The non-commutative dynamics can be regarded as an effective description of the…
In this paper, we give a classification of link diagrams on nonorientable surfaces up to region crossing changes.
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
We formulate Noncommutative Qauntum Field Theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No *-product is needed in this formulation and noncommutativity is carried by a modified Fourier…
We make some remarks on deformations over non-commutative base. We describe the base algebra of versal deformations using $T^1$ and $T^2$.
The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties…