C∗-algebras without idempotents

AbstractThe simplest statement of the main results are these: Let π be a free group on 2 generators. Let Cπ be the complex ring and L1π the ring extension to L1 sums. Then L1π contains no idempotents. Furthermore, if α ϵ Cπ, β ϵ L1π are nonzero, then αβ ≠ 0. The first result is in the direction of proving that a certain simple C∗-algebra has no idempotents yielding a counter-example to the suggestion that simple C∗-algebras are generated by their projections