Congruence-simplicity of Steinberg algebras of non-Hausdorff ample groupoids over semifields

2021/09/03 by Nam, Tran Giang, Zumbrägel, Jens
#16S99 #16Y60 #20L05 #22A22 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2109.01555

Abstract

We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids, extending the well-known characterizations when S is a field. We apply our congruence-simplicity results to tight groupoids of inverse semigroup representations associated to self-similar graphs.

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