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G. Cortiñas (2011)
Topics in algebraic and topological K$K$‐theory, 2008
(1992)
Suslin andM.Wodzicki,Excision in algebraicK-theory, Ann. ofMath
Jonathan Rosenberg (1997)
The Algebraic K-Theory of Operator AlgebrasK-theory, 12
Guillermo Cortiñas, A. Thom (2009)
Algebraic geometry of topological spaces IActa Mathematica, 209
P. Ara, Guillermo Cortiñas (2011)
Tensor products of Leavitt path algebrasarXiv: Rings and Algebras, 141
J. Kaminker, I. Putnam (1996)
K-Theoretic Duality for Shifts of Finite TypeCommunications in Mathematical Physics, 187
Iain Dangerfield (2017)
Leavitt Path Algebras
Guillermo Cortiñas, A. Thom (2006)
Bivariant algebraic K-theory, 2007
Guillermo Cortiñas, S. Vega (2020)
Bivariant Hermitian K-theory and Karoubi's fundamental theoremJournal of Pure and Applied Algebra
M. Karoubi, O. Villamayor (1971)
$K$-théorie algébrique et $K$-théorie topologique I.Mathematica Scandinavica, 28
(2005)
Comparison between algebraic and topological K-theory for Banach algebras and C-algebras, Handbook of K-theory, vol
Guillermo Cortiñas, N. Phillips (2014)
Algebraic K-theory and properly infinite C*-algebrasarXiv: K-Theory and Homology
M. Rørdam, E. Størmer (2001)
Classification of Nuclear C*-Algebras. Entropy in Operator Algebras
J. Wright (1990)
K-THEORY FOR OPERATOR ALGEBRAS: (Mathematical Sciences Research Institute Publications 5)Bulletin of The London Mathematical Society, 22
Guillermo Cortiñas, Diego Montero (2018)
Homotopy classification of Leavitt path algebrasAdvances in Mathematics, 362
G. Abrams, P. Ánh, A. Louly, E. Pardo (2007)
The classification question for Leavitt path algebrasarXiv: Rings and Algebras
M. Dadarlat, S. Eilers (1998)
On The Classification of Nuclear C*‐AlgebrasProceedings of the London Mathematical Society, 85
(1986)
Homologie de groupes discrets associés à des algèbres d'opérateurs
N. Phillips (1995)
A classification theorem for nuclear purely infinite simple $C^*$-algebrasDocumenta Mathematica
P. Ara, Miquel Brustenga, Guillermo Cortiñas (2009)
$K$-theory of Leavitt path algebrasarXiv: K-Theory and Homology
R. Meyer (2011)
Universal Coefficient Theorems and Assembly Maps in KK-Theory
G. Abrams, A. Louly, E. Pardo, C. Smith (2008)
Flow invariants in the classification of Leavitt path algebrasarXiv: Rings and Algebras
Guillermo Cortiñas (2009)
Algebraic v. Topological K-Theory:A Friendly MatcharXiv: K-Theory and Homology
B. Blackadar (1986)
K-Theory for Operator Algebras
(2016)
Category theory in context, Aurora
(1987)
Homotopy algebraic -theory, Algebraic -theory and algebraic number theory
Guillermo Cortiñas (2021)
Classifying Leavitt path algebras up to involution preserving homotopyMathematische Annalen, 386
A. Suslin, M. Wodzicki (1992)
Excision in algebraic $K$-theoryAnnals of Mathematics, 136
Guillermo Cortiñas, Diego Montero (2018)
Algebraic bivariant $K$-theory and Leavitt path algebras.arXiv: K-Theory and Homology
Let ξ:C∗(E)→C∗(F)$\xi :C^*(E)\rightarrow C^*(F)$ be a unital ∗$*$‐homomorphism between simple purely infinite Cuntz–Krieger algebras of finite graphs. We prove that there exists a unital ∗$*$‐homomorphism ϕ:L(E)→L(F)$\phi :L(E)\rightarrow L(F)$ between the corresponding Leavitt path‐algebras such that ξ$\xi$ is homotopic to the map ϕ̂:C∗(E)→C∗(F)$\hat{\phi }:C^*(E)\rightarrow C^*(F)$ induced by completion. We show moreover that ϕ̂$\hat{\phi }$ is a homotopy equivalence in the C∗$C^*$‐algebraic sense if and only if ϕ$\phi$ is a homotopy equivalence in the algebraic, polynomial sense. We deduce, in particular, that any isomorphism between simple purely infinite Cuntz–Krieger algebras is homotopic to the completion of a unital algebraic homotopy equivalence.
Bulletin of the London Mathematical Society – Wiley
Published: Dec 1, 2022
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