Ideal structure of Nica-Toeplitz algebras. (English) Zbl 07846496
Summary: We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra \(\mathcal{NT}(X)\) of a product system \((A, X)\) over \(\mathbb{N}^n\). We obtain a clear description of \(X\)-invariant ideals in \(A\), that is, restrictions of gauge-invariant ideals in \(\mathcal{NT}(X)\) to \(A\). The main result is a classification of gauge-invariant ideals in \(\mathcal{NT}(X)\) for a proper product system in terms of families of ideals in \(A\). We also apply our results to higher-rank graphs.
Keywords:
product systems; gauge-invariant ideals; Nica covariance; Nica-Pimsner algebras; higher-rank graphsReferences:
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