Representations of a k-algebra over the rational functions over k

For Λ a finite-dimensional k-algebra, k a field, we study the relations between the category of all left Λ-modules, Mod Λ, and the category of finitely generated Λ⊗ k k( x)= Λ k( x) -modules, mod Λ k( x) . In particular, we consider those G∈mod Λ k( x) such that Λ G is indecomposable. We prove that...

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Bibliographic Details
Published in:Journal of algebra 2003-09, Vol.267 (1), p.342-358
Main Authors: Bautista, Raymundo, Yingbo, Zhang
Format: Article
Language:English
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Summary:For Λ a finite-dimensional k-algebra, k a field, we study the relations between the category of all left Λ-modules, Mod Λ, and the category of finitely generated Λ⊗ k k( x)= Λ k( x) -modules, mod Λ k( x) . In particular, we consider those G∈mod Λ k( x) such that Λ G is indecomposable. We prove that such modules are in the mouth of components in mod Λ k( x) which are tubes or have the shape ZA ∞ , ZD ∞ , or ZB ∞ .
ISSN:0021-8693
1090-266X
DOI:10.1016/S0021-8693(03)00371-5