Algebraic Cartan pairs over ample etale groupoids

Ying-Fen Lin (Queen's University Belfast)

Thursday 27th April 16:00-17:00 Maths 311B


Groupoid C*-algebras and twisted groupoid C*-algebras were introduced by Renault in the late ’70, and have since proved extremely important in the study of structural properties for large classes of C*-algebras. Moreover, Kumjian and Renault developed the C*-algebraic theory of Cartan pairs which arise from twisted groupoid algebras of effective etale groupoids, and the groupoid and twist are uniquely (up to equivalence) determined. In my talk, I will introduce a purely algebraic analogue of Cartan pairs which we call algebraic Cartan, and I will give a correspondence between such pairs and twists over effective etale groupoids.

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