Σ-pure-injective modules for string algebras and linear relations

2017/05/29 by Raphael Bennett‐Tennenhaus, William Crawley-Boevey, Bennett-Tennenhaus, Raphael +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1705.10145

Abstract

We prove that indecomposable \Σ-pure-injective modules for a string\nalgebra are string or band modules. The key step in our proof is a splitting\nresult for infinite-dimensional linear relations.\n

Related

• Ringel's conjecture for domestic string algebras
• A simple homological characterization of string algebras of finite representation type
• Classification of modules for infinite-dimensional string algebras
• On extensions for gentle algebras
• Σ-pure-injectives in homotopy categories for gentle algebras