Ideal Structure of Nica-Toeplitz Algebras

Boris Bilich

doi:10.1007/s00020-024-02761-y

Ideal Structure of Nica-Toeplitz Algebras

Boris Bilich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra NT(X) of a product system (A, X) over Nⁿ. We obtain a clear description of X-invariant ideals in A, that is, restrictions of gauge-invariant ideals in NT(X) to A. The main result is a classification of gauge-invariant ideals in NT(X) for a proper product system in terms of families of ideals in A. We also apply our results to higher-rank graphs.

Original language	English
Article number	12
Journal	Integral Equations and Operator Theory
Volume	96
Issue number	2
DOIs	https://doi.org/10.1007/s00020-024-02761-y
State	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

46L08
46L55
Gauge-invariant ideals
Higher-rank graphs
Nica covariance
Nica-Pimsner algebras
Product systems

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-024-02761-y

Cite this

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title = "Ideal Structure of Nica-Toeplitz Algebras",

abstract = "We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra NT(X) of a product system (A, X) over Nn. We obtain a clear description of X-invariant ideals in A, that is, restrictions of gauge-invariant ideals in NT(X) to A. The main result is a classification of gauge-invariant ideals in 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 = "46L08, 46L55, Gauge-invariant ideals, Higher-rank graphs, Nica covariance, Nica-Pimsner algebras, Product systems",

author = "Boris Bilich",

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N2 - We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra NT(X) of a product system (A, X) over Nn. We obtain a clear description of X-invariant ideals in A, that is, restrictions of gauge-invariant ideals in NT(X) to A. The main result is a classification of gauge-invariant ideals in NT(X) for a proper product system in terms of families of ideals in A. We also apply our results to higher-rank graphs.

AB - We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra NT(X) of a product system (A, X) over Nn. We obtain a clear description of X-invariant ideals in A, that is, restrictions of gauge-invariant ideals in NT(X) to A. The main result is a classification of gauge-invariant ideals in NT(X) for a proper product system in terms of families of ideals in A. We also apply our results to higher-rank graphs.

KW - 46L08

KW - 46L55

KW - Gauge-invariant ideals

KW - Higher-rank graphs

KW - Nica covariance

KW - Nica-Pimsner algebras

KW - Product systems

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SN - 0378-620X

VL - 96

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

M1 - 12

ER -

Ideal Structure of Nica-Toeplitz Algebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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