|Title||Graded Steinberg algebras and their representations|
|Presenter||Huanhuan Li (University of Western Sydney)|
|Author(s)||Dr Huanhuan li|
|Session||Category Theory, Algebraic Topology, K-Theory|
We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. We show that this category is isomorphic to the category of unital left modules over the Steinberg algebra of the skew-product groupoid arising from the grading. To do this, we show that the Steinberg algebra of the skew product is graded isomorphic to a natural generalisation of the the Cohen--Montgomery smash product of the Steinberg algebra of the underlying groupoid with the grading group. This is joint work with Pere Ara, Roozbeh Hazrat, Aidan Sims.