The reduced group C*-algebra of a triangle building

Let Δ be an affine building of type Ã2 and let Γ be a discrete group of type-rotating automorphisms acting simply transitively on the vertices of δ. We prove that the reduced group C*-algebra is simple. To prove this result we use the sufficient condition for the simplicity of given in a recent paper by M. Bekka, M. Cowling and P. de la Harpe.

On projective Hjelmslev planes of level n

In this paper, we establish a new (but equivalent) definition of projective Hjelmslev planes of level n. This shows that the nth floor of a triangle building is a projective Hjelmslev plane of level n (a result already announced in [9], but left unproved). This will allow us to characterize Artmann-sequences by means of their inverse limits and to construct new ones. We also deduce a new existence theorem for level n projective Hjelmslev planes. All results hold in the finite as well as in the infinite case.