The interplay between Steinberg algebras and partial skew rings

2017/05/31 by Viviane Beuter, Daniel Gonçalves, Beuter, Viviane +1 · 1 citation
Mathematics · #16W22 #16W55 #22A22 #47L40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1706.00127

openalex publication_date 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the interplay between Steinberg algebras and partial skew rings: For a partial action of a group in a Hausdorff, locally compact, totally disconnected topological space, we realize the associated partial skew group ring as a Steinberg algebra (over the transformation groupoid attached to the partial action). We then apply this realization to characterize diagonal preserving isomorphisms of partial skew group rings, over commutative algebras, in terms of continuous orbit equivalence of the associated partial actions. Finally, we show that any Steinberg algebra, associated to a Hausdorff ample groupoid, can be seen as a partial skew inverse semigroup ring.

Citations

• C*-actions of r-discrete groupoids and inverse semigroups

Cited by

• Graded Steinberg algebras and partial actions

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