Irreducible Morphisms Between Modules over a Repetitive Algebras
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We describe the irreducible morphisms in the category of modules over a repetitive algebra. We find three special canonical forms: The first canonical form happens when all the component morphisms are split monomorphisms, the second when all the component morphisms are split epimorphisms and the third when there is exactly one irreducible component map. Also, we obtain the same result for the irreducible homomorphisms in the stable category of modules over a repetitive algebra.
KeywordsRepresentation theory of algebras Irreducible morphisms and repetitive algebras
Mathematics Subject Classification (2010)16G10 16G70
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We acknowledge the important collaboration and many, very helpful comments and suggestions of Raymundo Bautista for this work. The results presented here were obtained while the author were visiting the Centro de Ciencias de Matemáticas, UNAM, Unidad Morelia, for whose hospitality I am very grateful. We are deeply thankful to the reviewer(s) for his(hers) (theirs) remarks and suggestions, wich enabled us to improve this article.