2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231069The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the uniqueness of tracial state on the aforementioned C*-algebra.42 pages; In previous versions, statement of Proposition 2.11 was erroneous. Here is the list of resulting corrections: statement and proof of Proposition 2.11; Remark 2.12; statements of Proposition 2.17 and Theorems 6.4 and 6.5; proof of Theorem 6.3; addition of Lemma 6.6Group TheoryOperator Algebras22D25 (Primary) 46L05 (Secondary)text