Related papers: Generalized 2-vector spaces and general linear 2-g…
Spatial noncommutativity is similar and can even be related to the non-Abelian nature of multiple D-branes. But they have so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…
For a countable abelian group $G$ we investigate generic properties of the space of all invariant metrics on $G$. We prove that for every such an unbounded group $G$, i.e. group which has elements of arbitrarily high order, there is a dense…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
We introduce a notion of ``$n$-dual'' to a simplicial vector space for $n\ge 0$. Coming with it, there is a canonical pairing, which we show to be non-degenerate up to homotopy for homotopy $n$-types. As a result this notion of duality is…
Given a topological group $G$ that can be embedded as a topological subgroup into some topological vector space (over the field of reals) we say that $G$ has invariant linear span if all linear spans of $G$ under arbitrary embeddings into…
Given a compact Lie group $G$ and an orthogonal $G$-representation $V$, we give a purely metric criterion for a closed subset of the orbit space $V/G$ to have convex pre-image in $V$. In fact, this also holds with the natural quotient map…
We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct…
In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a…
We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification…
Let $U$ be a finite dimentional vector space over $\mathbb R$ or $\mathbb C$, and let $\rho:G\to GL(U)$ be a representation of a connected Lie group $G$. A linear subspace $V\subset U$ is called universal if every orbit of $G$ meets $V$. We…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This generalizes and strengthens several former results…
In this paper we present a unified proof of the fact that the category of modules over a ring and the category of near-vector spaces in the sense of J. Andr\'e, over an appropriate scalar system (a 'scalar group'), are both abelian…
In recent papers and books, a global quantization has been developed for unimodular groups of type I. It involves operator-valued symbols defined on the product between the group $\mathsf{G}$ and its unitary dual $\widehat{\mathsf{G}}$,…
We introduce the notion of a naive global 2-ring: a functor from the opposite of the $\infty$-category of global spaces to presentably symmetric monoidal stable $\infty$-categories. By passing to global sections, every naive global 2-ring…
Cell structures were introduced by W. Debski and E. Tymchatyn as a way to study some classes of topological spaces and their continuous functions by means of discrete approximations. In this work we weaken the notion of cell structure and…
We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski…
We consider the category $\mathbf{AOVS}$ of Archimedean ordered vector spaces with linear maps which preserve all existing suprema, and its full subcategories $\mathbf{DAOVS}$, $\mathbf{DVL}$ and $\mathbf{UVL}$, consisting of directed…