We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori...

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

We formulate a new class of tensor gauge field theories in any dimension that is hybrid between symmetric higher-rank theory (i.e., higher-spin theory) and anti-symmetric topological theory. Our describes mixed unitary phase interplaying gapless gapped order phases (which can live with or without Euclidean, Poincar\'e anisotropic symmetry, at least ultraviolet high intermediate energy theory, b...

Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

We introduce a non-Abelian tensor multiplet directly in the loop space associated with flat six-dimensional Minkowski space-time, and derive the supersymmetry variations for on-shell N = (2, 0) supersymmetry. [email protected]

Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

To understand the Abelian dominance and magnetic monopole dominance in lowenergy QCD, we rewrite the non-Abelian Wilson loop into the form which is written in terms of its Abelian components or the ’t Hooft-Polyakov tensor describing the magnetic monopole. This is peformed by making use of a version of non-Abelian Stokes theorem. We propose a modified version of the maximal Abelian (MA) gauge. ...