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

Autor:	Abrams, Gene, Dokuchaev, Mikhailo, Nam, T. G.
Rok vydání:	2019
Předmět:	Mathematics - Rings and Algebras 16S99 05C25 46L
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.03964 Zobrazit plný text záznamu View this record from Arxiv