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arXiv · 1503.03046

Regular Representations of Lattice Ordered Semigroups

Boyu Li
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Abstract

We establish a necessary and sufficient condition for a representation of a 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.

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Boyu Li. 2015-03-10. Regular Representations of Lattice Ordered Semigroups. https://arxiv.org/abs/1503.03046

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