Related papers: Born's group and Generalized isometries
In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian…
We define an Isometry germ at any given event $x$ of space-time as a vector field $\xi$ defined in a neighborhood of $x$ such that the Lie derivative of both the metric and the Riemannian connection are zero at this event. Two isometry…
Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…
Colombeau generalized functions invariant under smooth (additive) one-parameter groups are characterized. This characterization is applied to generalized functions invariant under orthogonal groups of arbitrary signature, such as groups of…
A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate…
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a…
This paper allows one to obtain a criterion for the existence of a projectively invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). Such necessary and sufficient…
We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimensional Lie groups. The finite dimensional examples are the…
For $\mathrm{O}(\mathrm{q},k)$, the orthogonal group over a field $k$ of characteristic 2 with respect to a quadratic form $\mathrm{q}$, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either…
Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of…
A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based…
This article is a partial answer to the question of which groups can be represented as isometry groups of formal languages for generalized Levenshtein distances. Namely, it is proved that for any language the modulus of the difference…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
A dimension group is an ordered abelian group that is an inductive limit of a sequence of simplicial groups, and a stationary dimension group is such an inductive limit in which the homomorphism is the same at every stage. If a simple…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
The Cremona group is the group of birational transformations of the plane. A birational transformation for which there exists a pencil of lines which is sent onto another pencil of lines is called a Jonqui\`eres transformation. By the…
The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) transformation in local quantum physics. Our observables are…
Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a…
Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…
Suggested theory involves a drastic revision of a role of local internal symmetries in physical concept of curved geometry. Under the reflection of fields and their dynamics from Minkowski to Riemannian space a standard gauge principle of…