Classifying Leavitt path algebras up to involution preserving homotopy
Abstract
We prove that the Bowen-Franks group classifies the Leavitt path algebras of purely infinite simple finite graphs over a regular supercoherent commutative ring with involution where is invertible, equipped with their standard involutions, up to matricial stabilization and involution preserving homotopy equivalence. We also consider a twisting of the standard involution on Leavitt path algebras and obtain partial results in the same direction for purely infinite simple graphs. Our tools are -theoretic, and we prove several results about (Hermitian, bivariant) -theory of Leavitt path algebras.
Cite
@article{arxiv.2101.05777,
title = {Classifying Leavitt path algebras up to involution preserving homotopy},
author = {Guillermo Cortiñas},
journal= {arXiv preprint arXiv:2101.05777},
year = {2021}
}
Comments
39 pages, no figures. Second version is fully re-written. Third version clarifies the relevance of classic results of Joachim Cuntz to the present work. Fourth version corrects a typo and adds reference to Cuntz' homotopy classification of Cuntz-Krieger algebras [20]