Using the Steinberg algebra model to determine the center of any Leavitt path algebra
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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- G. Abrams, P. Ara and M. Siles Molina, Leavitt Path Algebras, Lecture Notes in Mathematics, Vol. 2191, Springer, London, 2017.Google Scholar
- J. Renault, A Groupoid Approach to C*-algebras, Lecture Notes in Mathematics, Vol. 793, Springer, Berlin, 1980.Google Scholar