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On Extensions for Gentle Algebras

Part of: Algebraic combinatorics Abelian categories Homological methods Representation theory of rings and algebras

Published online by Cambridge University Press:  28 January 2020

İlke Çanakçı ,
David Pauksztello  and
Sibylle Schroll
İlke Çanakçı
Affiliation:
Department of Mathematics, VU Amsterdam, Amsterdam 1081 HV, The Netherlands Email: i.canakci@vu.nl
David Pauksztello
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom Email: d.pauksztello@lancaster.ac.uk
Sibylle Schroll
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom Email: schroll@leicester.ac.uk
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Abstract

We give a complete description of a basis of the extension spaces between indecomposable string and quasi-simple band modules in the module category of a gentle algebra.

Keywords

gentle algebraextensionsbounded derived categoryhomotopy string and bandsstring combinatorics

MSC classification

Primary: 16G10: Representations of Artinian rings 16E35: Derived categories 18E30: Derived categories, triangulated categories 05E10: Combinatorial aspects of representation theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 1 , February 2021 , pp. 249 - 292
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

This work has been supported by the EPSRC through the grants EP/K026364/1, EP/K022490/1 and EP/N005457/1. The third author is supported by the EPSRC through an Early Career Fellowship EP/P016294/1.

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