We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain complete characterization congruence-simpleness for Steinberg algebras second-countable groupoids, extending well-known characterizations when S is field. apply our congruence-simplicity results to tight groupoids inverse semigroup representations associated self-similar graphs.

We present a new, geometric perspective on the recently proposed triality of 2d $\mathcal{N}=(0,1)$ gauge theories, based its engineering in terms D1-branes probing Spin(7) orientifolds. In this context, translates into fact that multiple theories correspond to same underlying orientifold. show how orientifolds particular involution, which we call universal give rise precisely original version ...

Introduction. Group representations occupy a sort of middle ground between abstract groups and transformation groups, i.e., groups acting in concrete ways as permutations of sets, homeomorphisms of topological spaces, diffeomorphisms of manifolds, etc. The requirement that the elements of a group act as linear operators on a vector space limits somewhat the complexity of the action without sacr...

The Bose–Fermi recoupling of particles arising from the Z2–grading of the irreducible representations of SU(2) is responsible for the Pauli exclusion principle. We demonstrate from fundamental physical assumptions how to extend this to gradings, other than the Z2 grading, arising from other groups. This requires non–associative recouplings where phase factors arise due to rebracketing of states...