Universal $C^∗$-algebras with the local lifting property - Courtney, Kristin E. (MATHEMATICA SCANDINAVICA, 2021)
The Local Lifting Property (LLP) is a localized version of projectivity for completely positive maps between $C^*$-algebras. Outside of the nuclear case, very few $C^*$-algebras are known to have the LLP\@. In this article, we show that the LLP holds for the algebraic contraction $C^*$-algebras introduced by Hadwin and further studied by Loring and Shulman. We also show that the universal Pythagorean $C^*$-algebras introduced by Brothier and Jones have the Lifting Property.