2021/07/20 by Raphael Bennett‐Tennenhaus, Bennett-Tennenhaus, Raphael
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2107.09529
openalex publication_date 2021/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify finitely generated modules over a class of algebras introduced in the authors' Ph.D thesis, called complete gentle algebras. These rings generalise the finite-dimensional gentle algebras introduced by Assem and Skowroński, in such a way so that the ground field is replaced by any complete local noetherian ring. Our classification is written in terms of string and band modules. For the proof we apply the main result from the authors' thesis, which classifies complexes of projective modules with finitely generated homogeneous components up to homotopy. In doing so we construct the resolution of a string or band module, generalising some calculations due to Çanakçi, Pauksztello and Schroll.