Operator algebras of higher rank numerical semigroups

Kakariadis, Evgenios; Katsoulis, Elias; Li, Xin

doi:10.1090/proc/15096

Operator algebras of higher rank numerical semigroups
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by Evgenios T.A. Kakariadis, Elias G. Katsoulis and Xin Li

Proc. Amer. Math. Soc. 148 (2020), 4423-4433

DOI: https://doi.org/10.1090/proc/15096

Published electronically: July 20, 2020

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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 in 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.

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