Related papers: A generalization of the Askey-Wilson relations usi…
Let $X$ be a finite set. A family $P$ of subsets of $X$ is called a convex geometry with ground set $X$ if (1) $\emptyset, X\in P$; (2) $A\cap B\in P$ whenever $A,B\in P$; and (3) if $A\in P$ and $A\neq X$, there is an element $\alpha\in…
We develop a generalized projective gauge theory of gravity and spinorial matter, incorporating both non-metricity and torsion. The work is divided into three parts. Part I provides a thorough review of General Relativity, Metric-Affine…
We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined…
This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, "p-typical" Witt vectors of p-adic schemes of finite type are already reasonably well understood. The main point here is to generalize this…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out…
Let M be a family of sequences (a_1,...,a_p) where each a_k is a flat in a projective geometry of rank n (dimension n-1) and order q, and the sum of ranks, r(a_1) + ... + r(a_p), equals the rank of the join a_1 v ... v a_p. We prove upper…
Given an automorphism and an anti-automorphism of a semigroup of a Geometric Algebra, then for each element of the semigroup a (generalized) projection operator exists that is defined on the entire Geometric Algebra. A single fundamental…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with…
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…
To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…
Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…
This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…
We generalize parts of the theory of associative geometries developed by Kinyon and the author in the framework of universal algebra: we prove that certain associoid structures, such as pregroupoids and principal equivalence relations, have…
Dual to Koldobsky's notion of j-intersection bodies, the class of j-projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j-projection bodies…
In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…
Racah and Wilson polynomials with dilated and translated argument are reparametrized such that the polynomials are continuous in the parameters as long as these are nonnegative, and such that restriction of one or more of the new parameters…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the $M$ theory on noncommutative tori. This…