Work

Unital aligned shift equivalence and the graded classification conjecture for Leavitt path algebras

Year: 2025

Type: article

Abstract: We prove that a unital shift equivalence induces a graded isomorphism of Leavitt path algebras when the shift equivalence satisfies an alignment condition. This yields another step towards confirming the Graded Classification Conjecture. Our proof uses the bridging bimodule developed by Abrams, the fourth-named author and Tomforde, as well as a general lifting result for graded rings that we establish here. This general result also allows us to provide simplified proofs of two important recent results: one independently proven by Arnone and Vaš through other means that the graded K-theory functor is full, and the other proven by Arnone and Cortiñas that there is no unital graded homomorphism between a Leavitt algebra and the path algebra of a Cuntz splice.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-025-03748-0

Authors: Kevin Aguyar Brix, Adam Dor-On, Roozbeh Hazrat, Efren Ruiz

Institutions: University of Southern Denmark, University of Haifa, Western Sydney University, University of Hawaii System, University of Hawaii at Hilo

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290