Meet Irreducible Ideals and Representations of Limit Algebras

Details Meet Irreducible Ideals and Representations of Limit Algebras Meet Irreducible Ideals and Representations of Limit Algebras

2002-06-24

arxiv.org/abs/math/0206252v1

Mathematics

Operator Algebras

8 pages; accepted in JFA

Scientific paper

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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