Operator algebras of higher rank numerical semigroups
Operator Algebras
2020-03-17 v2 Functional Analysis
Abstract
A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are known to provide examples that answer Arveson's Dilation Problem to the negative. Here we show that these algebras share the polydisc as the character space in a canonical way. We subsequently use this feature in order to identify higher rank numerical semigroups from the corresponding nonselfadjoint algebras.
Keywords
Cite
@article{arxiv.1902.03599,
title = {Operator algebras of higher rank numerical semigroups},
author = {Evgenios T. A. Kakariadis and Elias G. Katsoulis and Xin Li},
journal= {arXiv preprint arXiv:1902.03599},
year = {2020}
}
Comments
10 pages, minor corrections