Module theory over Leavitt path algebras and K-theory

2009/05/23 by Pere Ara, Ara, Pere, Miquel Brustenga +1 · 1 citation
Mathematics · #16D70 #16D90 #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) #math.KT #math.RA #msc:16D70 #msc:16D90

paper · pdf · doi:10.48550/arxiv.0905.3827

31 pages

arxiv created 2009/05/23 · openalex publication_date 2009/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field and let E be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra L_k (E) and show its close relationship with the finite-dimensional representations of the inverse quiver E of E, as well as with the class of finitely generated P_k(E)-modules M such that \rm Tor_q^{P_k (E)}(k^|E0|,M)=0 for all q, where P_k(E) is the usual path algebra of E. By using these results we compute the higher K-theory of the von Neumann regular algebra Q_k (E)=L_k (E)Σ^-1, where Σ is the set of all square matrices over P_k (E) which are sent to invertible matrices by the augmentation map ε\colon P_k (E)→ k^|E0|.

Citations

• Mixed quiver algebras
• Noncommutative localization and chain complexes I. Algebraic K- and L-theory

Cited by

• The Fox algebra, Localization and factorizations of free polynomials

Related

• Representations of Leavitt Path Algebras
• The regular algebra of a quiver
• Finite Dimensional Representations of Leavitt Path Algebras
• Finite Dimensional Representations of Quivers with Oriented Cycles
• The injective Leavitt complex