Classifying Leavitt path algebras up to involution preserving homotopy.

GUILLERMO CORTIÑAS

MATHEMATISCHE ANNALEN

SPRINGER

Lugar: Berlin; Año: 2022

0025-5831

We prove that the Bowen-Franks group classifies the Leavitt path algebras ofpurely infinite simple finite graphs over a regular supercoherent commutativering with involution where 2 is invertible, equipped with their standardinvolutions, up to matricial stabilization and involution preserving homotopyequivalence. We also consider a twisting of the standard involution on Leavittpath algebras and obtain partial results in the same direction for purelyinfinite simple graphs. Our tools are K-theoretic, and we prove severalresults about (Hermitian, bivariant) K-theory of Leavitt path algebras.