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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Abrams, G. [1] ; Dokuchaev, M. [2] ; Nam, T. G. [3]
Total Authors: 3
Affiliation:
[1] Univ Colorado, Dept Math, Colorado Springs, CO 80907 - USA
[2] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo, SP - Brazil
[3] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi - Vietnam
Total Affiliations: 3
Document type: Journal article
Source: Journal of Algebra; v. 593, p. 72-104, MAR 1 2022.
Web of Science Citations: 0
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. (C) 2021 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 20/16594-0 - Non commutative rings and applications
Grantee:Francisco Cesar Polcino Milies
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/06538-6 - Leavitt path algebras, Steinberg algebras and partial actions
Grantee:Tran Giang Nam
Support Opportunities: Scholarships in Brazil - Post-Doctoral