On the socle of a class of Steinberg algebras
Copyright policy )On the socle of a class of Steinberg algebras
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.
13 pages
- University of Malaga Spain
Steinberg algebra, Álgebra, Socle, Rings and Algebras (math.RA), Mathematics - Operator Algebras, FOS: Mathematics, Algebras asociativas, 16S99, 22A22, 16D25, 16D70, 18B40, 46L55, 16S88, Mathematics - Rings and Algebras, Grupos topológicos, Operator Algebras (math.OA), Groupoid
Steinberg algebra, Álgebra, Socle, Rings and Algebras (math.RA), Mathematics - Operator Algebras, FOS: Mathematics, Algebras asociativas, 16S99, 22A22, 16D25, 16D70, 18B40, 46L55, 16S88, Mathematics - Rings and Algebras, Grupos topológicos, Operator Algebras (math.OA), Groupoid
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