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Operator algebras of higher rank numerical semigroups. (English) Zbl 07237846

Summary: 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.

MSC:

47L25 Operator spaces (= matricially normed spaces)
46L07 Operator spaces and completely bounded maps
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