GENERALIZED CARTAN SUBALGEBRAS

In the eighties, A. Kumjian obtained C* -diagonals, which is a C* -algebraic version of J. Feldman and C. Moore’s famous Theorem on Cartan subalgebras of von Neumann algebras. J. Renault had reached a generalization of the characterization of C*-diagonals. This article is intended to offer a version of Renault’s result in which the Cartan subalgebra is not necessarily commutative