Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras

TL;DR

This paper proves a weak version of Hazrat's conjecture, showing that a K-theoretic invariant can classify Leavitt path algebras up to graded isomorphism for all finite essential graphs.

Contribution

It establishes that a K-theoretic invariant classifies Leavitt path algebras up to graded isomorphism for finite essential graphs, advancing the understanding of their algebraic structure.

Findings

Weak version of Hazrat's conjecture proven

Invariant classifies Leavitt path algebras for finite essential graphs

Progress towards full classification conjecture

Abstract

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs.