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Strongly graded groupoids and strongly graded Steinberg algebras

Authors
  • Clark, Lisa Orloff
  • Hazrat, Roozbeh
  • Rigby, Simon
Publication Date
Jan 01, 2019
Identifiers
DOI: 10.1016/j.jalgebra.2019.03.030
OAI: oai:archive.ugent.be:8616807
Source
Ghent University Institutional Archive
Keywords
Language
English
License
Green
External links

Abstract

We study strongly graded groupoids, which are topological groupoids G equipped with a continuous, surjective functor κ:G→Γ, to a discrete group Γ, such that κ−1(γ)κ−1(δ) = κ−1(γδ), for all γ, δ ∈ Γ. We introduce the category of graded G-sheaves, and prove an analogue of Dade’s Theorem: G is strongly graded if and only if every graded G-sheaf is induced by a Gε-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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