Filling families and strong pure infiniteness

2015/03/30 by Kirchberg, Eberhard, Sierakowski, Adam
#46L35 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1503.08519

Abstract

We introduce filling families with matrix diagonalization as a refinement of the work by Rørdam and the first named author. As an application we improve a result on local pure infiniteness and show that the minimal tensor product of a strongly purely infinite C^*-algebra and a exact C^*-algebra is again strongly purely infinite. Our results also yield a sufficient criterion for the strong pure infiniteness of crossed products A\rtimes_φℕ by an endomorphism φ of A (cf. Theorem 7.6). Our work confirms that the special class of nuclear Cuntz-Pimsner algebras constructed by Harnisch and the first named author consist of strongly purely infinite C^*-algebras, and thus absorb O_∞ tensorially.

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• Cuntz-Krieger algebras for infinite matrices
• Purely infinite simple C^*-algebras arising from free product constructions
• Non-simple purely infinite rings
• Infinite Tensor Products of C₀(R): Towards a Group Algebra for R^∞
• Purely infinite C*-algebras arising from crossed products