Noncommutative Cartan \(\mathrm {C}^*\)-subalgebras
Noncommutative Cartan \(\mathrm {C}^*\)-subalgebras
We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product decomposition for a noncommutative Cartan subalgebra is unique. We relate the property of being a noncommutative Cartan subalgebra to aperiodic …