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We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras and of graphs and over a commutative ground ring . We approach this by studying the structure of such algebras under bivariant algebraic -theory , which is the universal homology theory with the properties above. We show that under very mild assumptions on , for a graph with finitely many vertices and reduced incidence matrix , the structure of in depends only on the groups Coker and Coker. We also prove that for Leavitt path algebras, has several properties similar to those that Kasparov's bivariant -theory has for -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and Schochet.
Cite this article
Guillermo Cortiñas, Diego Montero, Algebraic bivariant -theory and Leavitt path algebras.. J. Noncommut. Geom. 15 (2021), no. 1, pp. 113–146DOI 10.4171/JNCG/397