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arXiv · 2502.15574

On the socle of a class of Steinberg algebras

Lisa Orloff Clark·Cristóbal Gil Canto·Dolores Martín Barquero·Cándido Martín González·Iván Ruiz Campos
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Abstract

We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit space of the groupoid. We apply this to obtain results about the socle of Steinberg algebras under certain hypotheses. This encompasses known results about Leavitt path algebras and improves on Kumjian-Pask algebra results to include higher-rank graphs that are not row-finite.

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Lisa Orloff Clark, Cristóbal Gil Canto, Dolores Martín Barquero, Cándido Martín González, Iván Ruiz Campos. 2025-02-21. On the socle of a class of Steinberg algebras. https://arxiv.org/abs/2502.15574

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