Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 3, pp. 327-334 (2006)

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On the contracted $l^1$-algebra of a polycyclic monoid

M.J. Crabb and W.D. Munn

Department of Mathematics, University of Glasgow,
Glasgow, G12 8QW -- SCOTLAND, U.K.

Abstract: Let $P(X)$ denote the polycyclic monoid (Cuntz semigroup) on a nonempty set $X$ and let $A$ denote the Banach algebra $\emph{l}^1(P(X))/Z$, where $Z$ is the (closed) ideal spanned by the zero of $P(X)$. Then $A$ is primitive. Moreover, $A$ is simple if and only if $X$ is infinite.

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Electronic version published on: 7 Mar 2008.

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