Cartan subalgebras in uniform Roe algebras
Stuart White, Rufus Willett
Abstract
In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B\subseteq A of C^* -algebras is isomorphic to the canonical inclusion of \ell^\infty(X) inside a uniform Roe algebra C^*_u(X) associated to a metric space of bounded geometry. We obtain uniqueness results for “Roe Cartans” inside uniform Roe algebras up to automorphism when X coarsely embeds into Hilbert space, and up to inner automorphism when X has property A.
Topics & Concepts
MathematicsBounded functionPure mathematicsUniquenessAutomorphismHilbert spaceMetric spaceMetric (unit)Property (philosophy)Space (punctuation)Inner automorphismAlgebra over a fieldUniform boundednessInclusion (mineral)Uniform continuityDiscrete mathematicsExistential quantificationImage (mathematics)Advanced Operator Algebra ResearchHolomorphic and Operator TheoryAdvanced Topics in Algebra