2018/06/26 by Bachir Bekka, Bekka, Bachir
Mathematics · #22D10 #22D25 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1806.10110
openalex publication_date 2018/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Answering a question of J. Rosenberg, we construct the first examples of infinite characters on GLn(K) for a global field K and n≥ 2. The case n=2 is deduced from the following more general result. Let G a non amenable countable subgroup acting on locally finite tree X. Assume either that the stabilizer in G of every vertex of X is finite or that the closure of the image of G in \rm Aut(X) is not amenable. We show that G has uncountably many infinite dimensional irreducible unitary representations (π, H) of G which are traceable, that is, such that the C^*-subalgebra of B(H) generated by π(G) contains the algebra of the compact operators on H. In the case n≥ 3, we prove the existence of infinitely many characters for G=SLn(R), where n≥ 3 and R is an integral domain such that G is not amenable. In particular, the group SLn(Z) has infinitely many such characters for n≥ 2.