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• W2896971649 abstract "Answering a question of J. Rosenberg from [21], 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 group acting on a 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 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=GLn(R), when 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." @default.
• W2896971649 created "2018-10-26" @default.
• W2896971649 creator A5003113893 @default.
• W2896971649 date "2019-10-01" @default.
• W2896971649 modified "2023-10-09" @default.
• W2896971649 title "Infinite characters on GL(Q), on SL (Z), and on groups acting on trees" @default.
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• W2896971649 doi "https://doi.org/10.1016/j.jfa.2018.10.003" @default.
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