%0 Journal Article
%T Regular Representations of Lattice Ordered Semigroups
%A Boyu Li
%J Mathematics
%D 2015
%I arXiv
%X We establish a necessary and sufficient condition for a representation of an lattice ordered semigroup to be regular, in the sense that certain extensions are completely positive definite. This result generalizes a theorem due to Brehmer where the lattice ordered group was taken to be $\mathbb{Z}_+^\Omega$. As an immediate consequence, we prove that contractive Nica-covariant representations on lattice ordered semigroups are regular, and therefore, its minimal isometric dilation is also Nica-covariant. We also introduce an analog of commuting row contractions on lattice ordered group and show that such a representation is regular.
%U http://arxiv.org/abs/1503.03046v1