 

Ruy Exel
Noncommutative Cartan subalgebras of C*algebras view print


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


Abstract
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.


Acknowledgements
Partially supported by CNPq


Author information
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040900  Florianópolis  Brasil
r@exel.com.br

