Principal ideals in subalgebras of groupoid \(C^*\)-algebras.
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Publication:1850248
zbMATH Open1038.47045arXivmath/0104163MaRDI QIDQ1850248
Author name not available (Why is that?)
Publication date: 1 January 2003
Published in: (Search for Journal in Brave)
Abstract: The study of different types of ideals in non self-adjoint operator algebras has been a topic of recent research. This study focuses on principal ideals in subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is generated by a single element of the algebra. We look at subalgebras of r-discrete principal groupoid C*-algebras and prove that these algebras are principal ideal algebras. Regular canonical subalgebras of almost finite C*-algebras have digraph algebras as their building blocks. The spectrum of almost finite C*-algebras has the structure of an r-discrete principal groupoid and this helps in the coordinization of these algebras. Regular canonical subalgebras of almost finite C*-algebras have representations in terms of open subsets of the spectrum for the enveloping C*-algebra. We conclude that regular canonical subalgebras are principal ideal algebras.
Full work available at URL: https://arxiv.org/abs/math/0104163
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