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Meet Irreducible Ideals and Representations of Limit Algebras

Kenneth R. Davidson·Elias Katsoulis·Justin Peters
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Abstract

In this paper we give a criterion for an ideal of a TAF algebra to be meet irreducible. We show that an ideal $J$ of $A$ is meet irreducile if and only if the C$^*$-envelope of the quotient $A/J$ is primitive. In that case, A/J admits a nest representation which extends to a *-representation of the C$^*$-envelope for $A/J.$ We also characterize the meet irreducible ideals as the kernels of nest representations; this settles the question of whether the n-primitive and meet irreducible ideals coincide.

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BibTeXRIS

Kenneth R. Davidson, Elias Katsoulis, Justin Peters. 2002-06-24. Meet Irreducible Ideals and Representations of Limit Algebras. https://arxiv.org/abs/math/0206252

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