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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中文翻译：

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高阶数值半群的算子代数

摘要：较高阶数值半群是一个正锥，其半正规化与自由阿贝尔半群同构。已知相应的非自伴半群代数可以提供以负数回答Arveson扩张问题的示例。在这里，我们证明这些代数以规范的方式共享多碟作为字符空间。我们随后使用此功能，以便从相应的非自伴代数中识别出更高等级的数值半群。

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