The regular algebra of a quiver

Pere Ara; Miquel Brustenga

doi:10.1016/j.jalgebra.2006.10.013

The regular algebra of a quiver

Pere Ara, Miquel Brustenga

Departament de Matemàtiques

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Resum

Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra Q (E) in a functorial way. The algebra Q (E) is a universal localization of the usual path algebra P (E) associated with E. The monoid of isomorphism classes of finitely generated projective right Q (E)-modules is explicitly computed. © 2006 Elsevier Inc. All rights reserved.

Idioma original	Anglès
Pàgines (de-a)	207-235
Revista	Journal of Algebra
Volum	309
DOIs	https://doi.org/10.1016/j.jalgebra.2006.10.013
Estat de la publicació	Publicada - 1 de març 2007

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10.1016/j.jalgebra.2006.10.013

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https://www.scopus.com/pages/publications/33751429207

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title = "The regular algebra of a quiver",

abstract = "Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra Q (E) in a functorial way. The algebra Q (E) is a universal localization of the usual path algebra P (E) associated with E. The monoid of isomorphism classes of finitely generated projective right Q (E)-modules is explicitly computed. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

keywords = "Leavitt path algebra, Path algebra, Universal localization, Von Neumann regular ring",

author = "Pere Ara and Miquel Brustenga",

year = "2007",

month = mar,

day = "1",

doi = "10.1016/j.jalgebra.2006.10.013",

language = "English",

volume = "309",

pages = "207--235",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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T1 - The regular algebra of a quiver

AU - Ara, Pere

AU - Brustenga, Miquel

PY - 2007/3/1

Y1 - 2007/3/1

N2 - Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra Q (E) in a functorial way. The algebra Q (E) is a universal localization of the usual path algebra P (E) associated with E. The monoid of isomorphism classes of finitely generated projective right Q (E)-modules is explicitly computed. © 2006 Elsevier Inc. All rights reserved.

AB - Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra Q (E) in a functorial way. The algebra Q (E) is a universal localization of the usual path algebra P (E) associated with E. The monoid of isomorphism classes of finitely generated projective right Q (E)-modules is explicitly computed. © 2006 Elsevier Inc. All rights reserved.

KW - Leavitt path algebra

KW - Path algebra

KW - Universal localization

KW - Von Neumann regular ring

UR - https://www.scopus.com/pages/publications/33751429207

U2 - 10.1016/j.jalgebra.2006.10.013

DO - 10.1016/j.jalgebra.2006.10.013

M3 - Article

SN - 0021-8693

VL - 309

SP - 207

EP - 235

JO - Journal of Algebra

JF - Journal of Algebra

ER -

The regular algebra of a quiver

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