Pseudocompact C^*-algebras

2016/09/20 by Stephen Hardy, Hardy, Stephen
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1609.06275

Abstract

We study the class of pseudocompact C*-algebras, which are the logical limits of finite-dimensional C*-algebras. The pseudocompact C*-algebras are unital, stably finite, real rank zero, stable rank one, and tracial. We show that the pseudocompact C*-algebras have trivial K₁ groups and the Dixmier property. The class is stable under direct sums, tensoring by finite-dimensional C*-algebras, taking corners, and taking centers. We give an explicit axiomatization of the commutative pseudocompact C*-algebras. We also study the subclass of pseudomatricial C*-algebras, which have unique tracial states, strict comparison of projections, and trivial centers. We give some information about the K₀ groups of the pseudomatricial C*-algebras.

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