The Ideal Structure of Toeplitz Algebras

Abstract.

We investigate the ideal structure of the Toeplitz algebra \( \mathcal{T}(\Gamma) \) of a totally ordered abelian group \( \Gamma \). We show that the primitive ideals of \( \mathcal{T}(\Gamma) \) are parametrised by the disjoint union \( X \) of the duals \( \hat{I} \) of the order ideals \( I \) of \( \Gamma \), and identify the hull-kernel topology on \( X \) when the chain of orderideals in \( \Gamma \) is isomorphic to a subset of \( \{-\infty\}\cup \mathbb{Z} \cup \{\infty\} \)