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arXiv · 1604.01079

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

Lisa Orloff Clark·Dolores Martín Barquero·Cándido Martín González·Mercedes Siles Molina
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Abstract

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

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Lisa Orloff Clark, Dolores Martín Barquero, Cándido Martín González, Mercedes Siles Molina. 2016-04-04. Using the Steinberg algebra model to determine the center of any Leavitt path algebra. https://arxiv.org/abs/1604.01079

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