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arXiv · math/9911007

Purely infinite, simple C*-algebras arising from free product constructions, II

Ken Dykema
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Abstract

Certain reduced free products of C*-algebras, (A,phi)=(A_1,phi_1)*(A_2,ϕ_2), taken with respect to faithful states, at least one of which is not a trace, are shown to be purely infinite and simple. It is assumed that one of the A_i contain a partial isometry in the spectral subspace of phi_i corresponding to a positive number not equal to one. For example, if A_1 and A_2 are copies of the two-by-two complex matrices and if phi_1 and phi_2 are not unitarily conjugate, it is shown that A is simple and purely infinite.

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Ken Dykema. 1999-11-02. Purely infinite, simple C*-algebras arising from free product constructions, II. https://arxiv.org/abs/math/9911007

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