Graded Steinberg algebras
摘要：We consider the graded 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. Specialising to the setting of directed graphs, we produce a representation of the monoid of graded finitely generated projective modules over a Leavitt path algebra.