New York Journal of Mathematics
Volume 17 (2011) 331-382


Ruy Exel

Noncommutative Cartan subalgebras of C*-algebras

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Published: June 16, 2011
Keywords: C*-algebras, Cartan subalgebras, inverse semigroups, Fell bundles
Subject: Primary 46L45, secondary 46L55, 20M18

J. Renault has recently found a generalization of the characterization of C*-diagonals obtained by A. Kumjian in the eighties, which in turn is a C*-algebraic version of J. Feldman and C. Moore's well known theorem on Cartan subalgebras of von Neumann algebras. Here we propose to give a version of Renault's result in which the Cartan subalgebra is not necessarily commutative [sic]. Instead of describing a Cartan pair as a twisted groupoid C*-algebra we use N. Sieben's notion of Fell bundles over inverse semigroups which we believe should be thought of as twisted étale groupoids with noncommutative unit space. En passant we prove a theorem on uniqueness of conditional expectations.


Partially supported by CNPq

Author information

Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 - Florianópolis - Brasil