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

Autor(es)

Abrams, G. ^[1] ; Dokuchaev, M. ^[2] ; Nam, T. G. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 593, p. 72-104, MAR 1 2022.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 20/16594-0 - Anéis não comutativos e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/06538-6 - Álgebras de Leavitt de caminhos, álgebras de Steinberg e ações parciais.
• Beneficiário: Tran Giang Nam
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado