Maximal $n$-orthogonal modules for selfinjective algebras
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- by Karin Erdmann and Thorsten Holm PDF
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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.References
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Additional Information
- Karin Erdmann
- Affiliation: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
- MR Author ID: 63835
- ORCID: 0000-0002-6288-0547
- Email: erdmann@maths.ox.ac.uk
- 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
- Email: thorsten.holm@mathematik.uni-magdeburg.de, holm@math.uni-hannover.de
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3069-3078
- MSC (2000): Primary 16G10, 16D50, 16E10, 16G70
- DOI: https://doi.org/10.1090/S0002-9939-08-09297-6
- MathSciNet review: 2407069