We consider the problem of commutative rank computation of a given matrix space, B ⊆ Fn×n. The problem is fundamental, as it generalizes several computational problems from algebra and combinatorics. For instance, checking if the commutative rank of the space is n, subsumes problems such as testing perfect matching in graphs and identity testing of algebraic branching programs. An efficient det...

We present a candidate supergravity solution for a stacked configuration of stable non-BPS D-branes in Type II string theory compactified on T /Z2. This gives a supergravity description of nonabelian tachyon condensation on the brane worldvolume. BROWN-HET-1263 IC/2001/27

By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdSd+1 space. We have found that in the boundary of two layers AdSd+1 space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry. e-mail:kaviani,[email protected]...

We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter θ. Associated with C...

Four-dimensional quantum field theory suffers from infrared and ultraviolet divergences as well as from the divergence of the renormalised perturbation expansion. Despite early suggestions as to modify the space-time structure [1], quantum field theory on non-commutative spaces was studied in details only after Alain Connes developed noncommutative geometry [2]. The first steps were connected t...

A quantum deformation of the conformal algebra of the Minkowskian spacetime in (3 + 1) dimensions is identified with a deformation of the (4 + 1)-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known κ-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian sp...

Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of co...

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...