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

2012/10/11 by Pere Ara, Ara, P., Enrique Pardo +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 16D70 #Rings and Algebras (math.RA) #Secondary 46L55

paper · pdf · doi:10.48550/arxiv.1210.3127

openalex publication_date 2012/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Higher-rank graphs and the graded K-theory of Kumjian-Pask Algebras

Related

• A note on the isomorphism conjectures for Leavitt path algebras
• The classification question for Leavitt path algebras
• Graded isomorphisms of Leavitt path algebras and Leavitt inverse semigroups
• The graded structure of Leavitt Path algebras
• Graded homotopy classification of Leavitt path algebras