52 research outputs found
Strongly graded groupoids and strongly graded Steinberg algebras
We study strongly graded groupoids, which are topological groupoids equipped with a continuous, surjective functor , to a discrete group , such that
, for all
. We introduce the category of graded -sheaves, and prove an analogue of Dade's Theorem: is strongly
graded if and only if every graded -sheaf is induced by a -sheaf. The Steinberg algebra of a graded ample groupoid is
graded, and we prove that the algebra is strongly graded if and only if the
groupoid is. Applying this result, we obtain a complete graphical
characterisation of strongly graded Leavitt path and Kumjian-Pask algebras
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