GeNoCAS 2023: Bartosz K. Kwaśniewski

Noncommutative Cartan C*-subalgebras


Celebrated Renault’s result states that commutative Cartan C*-subalgebras, i.e. regular maximal abelian C*-subalgebras with faithful conditional expectation, are equivalent to topologically free twisted groupoids.

Recently, Exel generalized the notion of a Cartan inclusion to the case where the C*-subalgebra is an arbitrary (noncommutative) C*-algebra, and proved a part of a Renault’s theorem. In this talk I present a number

of characterisations of noncommutative Cartan C*-inclusions that fully generalize Renault’s Theorem, and give tools to study properties of the ambient algebra. (Based on a joint work with Ralf Meyer)