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arXiv · 2002.02365

Universal $\mathrm{C}^*$-algebras with the Local Lifting Property

Kristin E. Courtney
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Abstract

The Local Lifting Property (LLP) is a localized version of projectivity for completely positive maps between $\mathrm{C}^*$-algebras. Outside of the nuclear case, very few $\mathrm{C}^*$-algebras are known to have the LLP. In this article, we show that the LLP holds for the algebraic contraction $\mathrm{C}^*$-algebras introduced by Hadwin and further studied by Loring and Shulman. We also show that the universal Pythagorean $\mathrm{C}^*$-algebras introduced by Brothier and Jones have the Lifting Property.

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Kristin E. Courtney. 2020-02-06. Universal $\mathrm{C}^*$-algebras with the Local Lifting Property. https://arxiv.org/abs/2002.02365

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