2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99026Let (G,S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C-*-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C>0 and a natural number L such that for a function f in l^2(G) supported on elements of length n with respect to the generating set S: || f * h || <= C(n+1)^{3/2 L} || f || || h ||, forall h in l^2(G).15 pages, LaTeXOperator AlgebrasGroup Theory43A65; 46L99, 22D25, 20F55text