JournalsggdVol. 14, No. 3pp. 949–989

Cartan subalgebras in uniform Roe algebras

  • Stuart White

    Oxford University, UK
  • Rufus Willett

    University of Hawaii at Manoa, Honolulu, USA
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In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion BAB\subseteq A of CC^*-algebras is isomorphic to the canonical inclusion of (X)\ell^\infty(X) inside a uniform Roe algebra Cu(X)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 XX coarsely embeds into Hilbert space, and up to inner automorphism when XX has property A.

Cite this article

Stuart White, Rufus Willett, Cartan subalgebras in uniform Roe algebras. Groups Geom. Dyn. 14 (2020), no. 3, pp. 949–989

DOI 10.4171/GGD/570