On the Structure of Some Reduced Amalgamated Free Product C*-Algebras

Abstract

We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the latter result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag–Solitar groups BS(m, n).

Leavitt path algebras of separated graphs

“…There are representations λ ι : A ι → L(M) corresponding to the action of A ι on terms with left hand factor M ι , see for instance [31], [16], and * red…”

“…As in [22], we will use the following unitaries in M n (C). Let λ n be a primitive n-th root of 1, and set: We need for our next examples a slight generalization of Proposition 4.1 for reduced amalgamated products over C*-algebras different from C. Other generalizations to this context have been obtained in [22] and [16]. Assume there is a central projection P ∈ A 0 such that P A 0 = CP .…”

C * -simplicity of HNN extensions and groups acting on trees

“…Clearly, Γ is non-ascending if and only if min{|m|, |n|} 2. A result of the second author [20,Theorem 4.9] states that BS(m, n) is C * -simple if and only if min{|m|, |n|} 2 and |m| = |n|.…”

“…[11][12][13][14][15][16][17][18][19][20][21][22] Lemma 5.8] by the second and third author it was incorrectly stated that ∂T is always a Γ-boundary, which was later used the proof of[22, Theorem 5.9]. The statement of [22, Theorem 5.9] is still correct; in fact, a much more general result holds, as shown in Theorem 3.9.…”

On maximal ideals in certain reduced twisted C*-crossed products

“…We refer to [17] for a detailed overview of C * -simple groups and their properties. Some related articles written afterwards are [7,19,22,25,27,30,34].…”