info:eu-repo/semantics/article
Algebraic bivariant K-theory and Leavitt path algebras
Fecha
2021-02-02Registro en:
Cortiñas, Guillermo Horacio; Montero, Diego; Algebraic bivariant K-theory and Leavitt path algebras; European Mathematical Society; Journal of Noncommutative Geometry; 25; 1; 2-2-2021; 113-146
1661-6952
1661-6960
CONICET Digital
CONICET
Autor
Cortiñas, Guillermo Horacio
Montero, Diego
Resumen
We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We approach this by studying the structure of such algebras under bivariant algebraic K-theory kk, which is the universal homology theory with the properties above. We show that under very mild assumptions on `, for a graph E with finitely many vertices and reduced incidence matrix AE, the structure of L.E/ in kk depends only on the groups Coker.I AE/ and Coker.I A t E/. We also prove that for Leavitt path algebras, kk has several properties similar to those that Kasparov’s bivariant K-theory has for C -graph algebras, including analogues of the Universal coefficient and Künneth theorems of Rosenberg and Schochet