Maximal n-Orthogonal Modules for Selfinjective Algebras

Let A be a finite-dimensional selfinjective algebra. We show that, for any n ≥ 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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-09, Vol.136 (9), p.3069-3078
Main Authors: Erdmann, Karin, Holm, Thorsten
Format: Article
Language:English
Subjects:
Abstract algebra
Algebra
Automorphisms
Exact sciences and technology
General mathematics
General, history and biography
Mathematical theorems
Mathematics
Quaternion algebra
Quaternions
Sciences and techniques of general use
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Description
Summary:Let A be a finite-dimensional selfinjective algebra. We show that, for any n ≥ 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-08-09297-6