Purely infinite partial crossed products

Thierry Giordano; Adam Sierakowski

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arXiv · 1303.4483

Purely infinite partial crossed products

Thierry Giordano·Adam Sierakowski

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Abstract

Let (A,G,\alpha) be a partial dynamical system. We show that there is a bijective correspondence between G-invariant ideals of A and ideals in the partial crossed product A xr G provided the action is exact and residually topologically free. Assuming, in addition, a technical condition---automatic when A is abelian---we show that A xr G is purely infinite if and only if the positive nonzero elements in A are properly infinite in A xr G. As an application we verify pure infiniteness of various partial crossed products, including realisations of the Cuntz algebras O_n, O_A, O_N, and O_Z as partial crossed products.

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Thierry Giordano, Adam Sierakowski. 2013-03-19. Purely infinite partial crossed products. https://arxiv.org/abs/1303.4483

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