Universal $\mathrm{C}^*$algebras with the Local Lifting Property
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.02365
 Bibcode:
 2020arXiv200202365C
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 Minor changes, to appear in Math. Scand