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Classification of Symmetric Special Biserial Algebras With At Most One Non-Uniserial Indecomposable Projective

Published online by Cambridge University Press:  13 February 2015

Nicole Snashall  and
Rachel Taillefer
Nicole Snashall
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK (njs5@le.ac.uk)
Rachel Taillefer
Affiliation:
Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Complexe Universitaire des Cézeaux, 63171 Aubière, France (rachel.taillefer@math.univ-bpclermont.fr)
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Abstract

We consider a natural generalization of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the weakly symmetric algebras of Euclidean type n, as studied by Bocian et al., as well as some algebras of dihedral type.

Keywords

special biserial algebraderived equivalencestable equivalence of Morita typegeneralized Brauer tree algebraPrimary 16D5016E35Secondary 16E40
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 3 , October 2015 , pp. 739 - 767
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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