Classification of modules for complete gentle algebras

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 Skowro\'{n}ski, in such a way so that the ground field is replaced...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Author: Bennett-Tennenhaus, Raphael
Format: Article
Language:English
Subjects:
Algebra
Classification
Modules
Rings (mathematics)
Strings
Online Access:Get full text
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Summary: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 Skowro\'{n}ski, 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.
ISSN:2331-8422