Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C^*-algebras

2019/09/09 by Abrams, Gene, Dokuchaev, Mikhailo, Nam, T. G. · 1 citation
#05C25 #16S99 #46L #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1909.03964

Abstract

We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra L_K(E) of an arbitrary graph E with coefficients in a field K is isomorphic to a Steinberg algebra. This yields in particular that every nonzero corner of the Leavitt path algebra of an arbitrary graph is isomorphic to a Steinberg algebra. This in its turn gives that every K-algebra with local units which is Morita equivalent to the Leavitt path algebra of a row-countable graph is isomorphic to a Steinberg algebra. Moreover, we prove that a corner by a projection of a C^*-algebra of a countable graph is isomorphic to the C^*-algebra of an ample groupoid.

Cited by

• The Leavitt inverse semigroup of a separated graph

Related

• Corners of Leavitt path algebras of finite graphs are Leavitt path algebras
• The groupoid approach to Leavitt path algebras
• Realizing ultragraph Leavitt path algebras as Steinberg algebras
• Using the Steinberg algebra model to determine the center of any Leavitt\n path algebra
• A survey of some of the recent developments in Leavitt path algebras