Principal Ideals in Subalgebras of Groupoid C*-Algebras

Details Principal Ideals in Subalgebras of Groupoid C*-Algebras Principal Ideals in Subalgebras of Groupoid C*-Algebras

2001-04-17

arxiv.org/abs/math/0104163v2

Mathematics

Operator Algebras

20 pages

Scientific paper

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.

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