The socle series of a Leavitt path algebra

2009/06/23 by Gene Abrams, Abrams, Gene, Kulumani M. Rangaswamy +3
Mathematics · #16D60 #16S99 #46L89 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D60 #msc:16S99 #msc:46L89

paper · pdf · doi:10.48550/arxiv.0906.4376

15 pages

arxiv created 2009/06/23 · openalex publication_date 2009/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the ascending Loewy socle series of Leavitt path algebras L_K(E) for an arbitrary graph E and field K. We classify those graphs E for which L_K(E)=S_λ for some element S_λ of the Loewy socle series. We then show that for any ordinal λ there exists a graph E so that the Loewy length of L_K(E) is λ. Moreover, λ≤ ω (the first infinite ordinal) if E is a row-finite graph.

Related

• Socle theory for Leavitt path algebras of arbitrary graphs
• A survey of some of the recent developments in Leavitt path algebras
• Purely infinite simple Leavitt path algebras
• The Leavitt path algebra of a graph
• Stable rank of Leavitt path algebras of arbitrary graphs