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A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras

  • Lisa Orloff Clark , Ruy Exel EMAIL logo and Enrique Pardo
Published/Copyright: August 12, 2017

Abstract

Given an ample, Hausdorff groupoid 𝒢, and a unital commutative ring R, we consider the Steinberg algebra AR(𝒢). First we prove a uniqueness theorem for this algebra and then, when 𝒢 is graded by a cocycle, we study graded ideals in AR(𝒢). Applications are given for two classes of ample groupoids, namely those coming from actions of groups on graphs, and also to groupoids defined in terms of Boolean dynamical systems.


Communicated by Karl Strambach


Award Identifier / Grant number: 15-UOO-071

Award Identifier / Grant number: 301002/2015-0

Award Identifier / Grant number: FQM-298

Award Identifier / Grant number: MTM2014-53644-P

Award Identifier / Grant number: MTM2014-53644-P

Funding statement: The first-named author was partially supported by Marsden grant 15-UOO-071 from the Royal Society of New Zealand. The second-named author was partially supported by CNPq. The third-named author was partially supported by PAI III grant FQM-298 of the Junta de Andalucía, and by the DGI-MINECO and European Regional Development Fund, jointly, through grant MTM2014-53644-P.

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Received: 2016-9-12
Revised: 2017-4-4
Published Online: 2017-8-12
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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