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Proceedings of the American Mathematical Society

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Maximal $ n$-orthogonal modules for selfinjective algebras

Authors: Karin Erdmann and Thorsten Holm
Journal: Proc. Amer. Math. Soc. 136 (2008), 3069-3078
MSC (2000): Primary 16G10, 16D50, 16E10, 16G70
Published electronically: April 29, 2008
MathSciNet review: 2407069
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Abstract: Let $ A$ be a finite-dimensional selfinjective algebra. We show that, for any $ n\ge 1$, maximal $ n$-orthogonal $ A$-modules (in the sense of Iyama) rarely exist. More precisely, we prove that if $ A$ admits a maximal $ n$-orthogonal module, then all $ A$-modules are of complexity at most 1.

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Additional Information

Karin Erdmann
Affiliation: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom

Thorsten Holm
Affiliation: Institut für Algebra und Geometrie, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany – and – Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Address at time of publication: Leibniz Universität Hannover, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Welfengarten 1, 30167 Hannover, Germany

Keywords: Selfinjective algebras, maximal $n$-orthogonal modules.
Received by editor(s): August 8, 2006
Received by editor(s) in revised form: July 20, 2007
Published electronically: April 29, 2008
Additional Notes: We gratefully acknowledge the support of the Mathematisches Forschungsinstitut Oberwolfach through a Research in Pairs (RiP) project, and also the support through a London Mathematical Society Scheme 4 grant.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.