Universal C^*-algebras with the Local Lifting Property

2020/02/06 by Kristin Courtney, Courtney, Kristin E.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2002.02365

openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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