PORTUGALIAE MATHEMATICA Vol. 63, No. 3, pp. 327334 (2006) 

On the contracted $l^1$algebra of a polycyclic monoidM.J. Crabb and W.D. MunnDepartment 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. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
