Groups and Operator Algebras Seminar

Speaker:  Gilles de Castro (Federal University of Santa Catarina)

Title:  Continuous orbit equivalence for partial dynamical systems

Abstract:  Given a partial dynamical system, one can construct its transformation groupoid. We characterize when two transformation groupoids are isomorphic in terms of the continuous orbit equivalence of their corresponding partial dynamical systems. Under certain additional conditions, the isomorphism between these groupoids is also characterized via the isomorphism of their corresponding crossed products. Furthermore, we provide several necessary and sufficient conditions for a groupoid to be isomorphic to a transformation groupoid, and apply our results to the case of orthogonal and saturated partial actions. (Joint work with Eun Ji Kang)