Related papers: Dimension expanders via quiver representations

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.

This paper examines the problem of obtaining a $D(4)$-quadruple by adding a smaller element to a $D(4)$-triple. We prove some relations between elements of observed hypothetical $D(4)$-quadruples under which conjecture of the uniqueness of…

In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…

The current acceleration of the universe leads us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…

We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…

For an arbitrary quiver Q and dimension vector d we prove that the dimension of the space of cuspidal functions on the moduli stack of representations of Q of dimension d over a finite field F_q is given by a polynomial in q with rational…

Let $\pi$ be a finite dimensional unitary representation of a group $G$ with a generating symmetric $n$-element set $S\subset G$. Fix $\vp>0$. Assume that the spectrum of $|S|^{-1}\sum_{s\in S} \pi(s) \otimes \overline{\pi(s)}$ is included…

The emphasis in the developmet of theories with more than three spatial dimensions has recently shifted towards ``brane world'' picture, which assumes that ordinary matter (with possible exceptions of gravitons and other, hypothetic,…

We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…

We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…

We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…

We start with the recently conjectured 3d bosonization dualities and gauge global symmetries to generate an infinite sequence of new dualities. These equate theories with non-Abelian product gauge groups and bifundamental matter. We uncover…

Full generalization of Kasner metric for the case of $n+1$ dimensions and $m\le n+1$ essential variables is obtained. Any solution is defined by the corresponding constant matrix of Kasner parameters. This parameters form in euclidian space…

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put…

The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…