Universal $C^∗$-algebras with the local lifting property


  • Kristin E. Courtney




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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How to Cite

Courtney, K. E. (2021). Universal $C^∗$-algebras with the local lifting property. MATHEMATICA SCANDINAVICA, 127(2), 361–381. https://doi.org/10.7146/math.scand.a-126018