Tristan Bice (Czech Academy of Sciences)
Cartan subalgebras allow C*-algebras to be represented on effective twisted étale groupoids by utilising key properties of their normaliser semigroup. Isolating these key properties, we formulate an appropriate notion of "Cartan semigroup" that allows us to represent C*-algebras on even non-effective groupoids. To each such semigroup there is again a corresponding commutative "semi-Cartan subalgebra" although it may no longer be maximal commutative and, moreover, a single semi-Cartan subalgebra may arise from various different Cartan semigroups, which yield different groupoid representations. In this talk we will outline this generalised Weyl groupoid construction and compare it to some general Fell bundle representations previously investigated by the speaker. This is work in progress with Jonathan H. Brown, Lisa Orloff-Clark, Ying-Fen Lin and Kathryn McCormick.
