2025/12/08 by Donoso-Echenique, Miguel
#20M25 #20M30 #43A15 (Secondary) #43A20 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2512.07445
For a semigroup S and a right ℤ[S]-submodule J≤ ℤ[S]n, we study expansivity of the algebraic action of S induced on the Pontryagin dual of ℤ[S]n/J. We completely determine the class of semigroups for which expansivity of this action is characterized by the triviality of J^⊥, in terms of the existence of a finite subset K⊆ S such that S=KS. This condition is satisfied in particular by every monoid, and more generally by every semigroup with a left unital convolution Banach algebra, in which case we are able to extend the characterization of expansivity in terms of an invertibility condition when J is finitely generated. We also exhibit examples of non-unital semigroups satisfying the hypotheses of our results.