Using the Steinberg algebra model to determine the center of any Leavitt\n path algebra

2016/04/04 by Lisa Orloff Clark, Dolores Martı́n Barquero, Clark, Lisa Orloff +5 · 1 citation
Materials Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1604.01079

openalex publication_date 2016/04/04 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Given an arbitrary graph, we describe the center of its Leavitt path algebra\nover a commutative unital ring. Our proof uses the Steinberg algebra model of\nthe Leavitt path algebra. A key ingredient is a characterization of compact\nopen invariant subsets of the unit space of the graph groupoid in terms of the\nunderlying graph: an open invariant subset is compact if and only if its\nassociated hereditary and saturated set of vertices satisfies Condition (F). We\nalso give a basis of the center. Its cardinality depends on the number of\nminimal compact open invariant subsets of the unit space.\n

Cited by

• Maximal Commutative Subalgebras of Steinberg Algebras

Related

• Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C^*-algebras
• Simplicity of Leavitt path algebras via graded ring theory
• A note on the core of Steinberg algebras
• Leavitt path algebras with coefficients in a commutative ring
• Centers of path algebras, Cohn and Leavitt path algebras