A note on the isomorphism conjectures for Leavitt path algebras

2012/04/16 by Roozbeh Hazrat, Hazrat, R.
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1204.3366

openalex publication_date 2012/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K₀ classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^\gr₀ classifies them completely \citehazann. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^\gr₀-groups of their Leavitt path algebras are isomorphic then their K₀-groups are isomorphic as well.

Citations

• The classification question for Leavitt path algebras
• The graded Grothendieck group and the classification of Leavitt path algebras
• On the classification of nuclear C*-algebras

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