Regular Dilation and Nica-covariant Representation on Semigroups
Boyu Li · arXiv (Cornell University) · 2017
Regular dilation has recently been extended to graph product of N, where having a *-regular dilation is equivalent to having a minimal isometric Nica-covariant dilation. In this paper, we first extend the result to all quasi-lattice ordered semigroups, and establish a similar equivalence between *-regular dilation, minimal isometric Nica-covariant dilation, and a Brehmer-type condition. This can be applied to various quasi-lattice ordered semigroups. We then extend the result to the class of right LCM semigroups.