Algebraic bivariant -theory and Leavitt path algebras.
Guillermo Cortiñas
Universidad de Buenos Aires, ArgentinaDiego Montero
Universidad de Buenos Aires, Argentina
![Algebraic bivariant $K$-theory and Leavitt path algebras. cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-15-issue-1.png&w=3840&q=90)
Abstract
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. 113–146
DOI 10.4171/JNCG/397