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dc.contributor.author
Cortiñas, Guillermo Horacio  
dc.contributor.author
Montero, Diego  
dc.date.available
2021-10-20T12:06:13Z  
dc.date.issued
2020-03  
dc.identifier.citation
Cortiñas, Guillermo Horacio; Montero, Diego; Homotopy classification of Leavitt path algebras; Academic Press Inc Elsevier Science; Advances in Mathematics; 362; 3-2020; 1-26  
dc.identifier.issn
0001-8708  
dc.identifier.uri
http://hdl.handle.net/11336/144394  
dc.description.abstract
In this paper we address the classification problem for purely infinite simple Leavitt path algebras of finite graphs over a field ℓ. Each graph E has associated a Leavitt path ℓ-algebra L(E). There is an open question which asks whether the pair (K0(L(E)),[1L(E)]), consisting of the Grothendieck group together with the class [1L(E)] of the identity, is a complete invariant for the classification, up to algebra isomorphism, of those Leavitt path algebras of finite graphs which are purely infinite simple. We show that (K0(L(E)),[1L(E)]) is a complete invariant for the classification of such algebras up to polynomial homotopy equivalence. To prove this we further develop the study of bivariant algebraic K-theory of Leavitt path algebras started in a previous paper and obtain several other results of independent interest.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Academic Press Inc Elsevier Science  
dc.rights
info:eu-repo/semantics/restrictedAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
ALGEBRAIC HOMOTOPY  
dc.subject
BIVARIANT K-THEORY  
dc.subject
CLASSIFICATION  
dc.subject
LEAVITT PATH ALGEBRAS  
dc.subject
PURELY INFINITE SIMPLICITY  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Homotopy classification of Leavitt path algebras  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2021-09-07T18:37:37Z  
dc.journal.volume
362  
dc.journal.pagination
1-26  
dc.journal.pais
Estados Unidos  
dc.description.fil
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina  
dc.description.fil
Fil: Montero, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina  
dc.journal.title
Advances in Mathematics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0001870819305766?via%3Dihub  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.aim.2019.106961