Twisted Steinberg algebras

20/11/2020, 14:00 - 15:00 in online

Lin, Ying-Fen (Queen’s University Belfast)


Abstract:

Groupoid C*-algebras and twisted groupoid C*-algebras are introduced by Renault in the late ’70, where twisted groupoid C*-algebras are generalisation of groupoid C*-algebras in which multiplication and involution are twisted by a 2-cocycle on the groupoid. Twisted groupoid C*-algebras have since proved extremely important in the study of structural properties for large classes of C*-algebras. Thirty years later, Steinberg algebras are introduced independently by Steinberg and Clark, Farthing, Sims and Tomforde which are a purely algebraic analogue of groupoid C*-algebras. Steinberg algebras not only provide useful insight into the analytic theory of groupoid C*-algebras, they also give rise to interesting examples of *-algebras; for example, all Leavitt path algebras and Kumjian-Pask algebras can be realised as Steinberg algebras.

In this talk, I will first recall some relevant background on topological groupoids, continuous 2-cocycles and twisted groupoid C*-algebras, then I will introduce twisted Steinberg algebras which generalise the Steinberg algebras and provide a purely algebraic analogue of twisted groupoid C*-algebras.

This event will take place online. Please contact the colloquium organiser (Florian Pausinger) if you wish to attend.

Mathematical Sciences Research Centre