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Stable endomorphism algebras of modules over special biserial algebras

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Abstract.

 We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle algebra is gentle.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK (e-mail: jschroer@maths.leeds.ac.uk), , , , , , GB

    Jan Schröer

  2. Faculté de Mathématiques et CNRS (LAMFA UMR 6140), Université de Picardie Jules Verne, 33, rue St Leu, 80039 Amiens, France (e-mail: alexander.zimmermann@u-picardie.fr), , , , , , FR

    Alexander Zimmermann

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  1. Jan Schröer
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  2. Alexander Zimmermann
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Additional information

Received: 17 May 2002 / Published online: 16 May 2003

Mathematics Subject Classification (2000): 16E30, 16G20, 18E30.

We gratefully acknowledge support from the Volkswagen Foundation (RIP Program at Oberwolfach). The first author thanks the Nuffield Foundation (Grant Number NAL/00270/G) for financial support.

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Schröer, J., Zimmermann, A. Stable endomorphism algebras of modules over special biserial algebras. Math. Z. 244, 515–530 (2003). https://doi.org/10.1007/s00209-003-0492-4

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  • DOI: https://doi.org/10.1007/s00209-003-0492-4

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