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On indecomposable modules over directed algebras

Author: Peter Dräxler
Journal: Proc. Amer. Math. Soc. 112 (1991), 321-327
MSC: Primary 16G60; Secondary 16D60
MathSciNet review: 1062830
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Abstract: Generalizing a result of Bongartz we show that any nonsimple indecomposable module over a finite-dimensional $ k$-algebra $ A$ is an extension of an indecomposable and a simple module provided $ k$ is a field with more than two elements and $ A$ is representation directed. Our proof is based on fibre sums over simple modules and some known classification results on socle projective modules over peak algebras. In case the global dimension of $ A$ is at most 2 our methods also yield a description of the dimension vectors of the indecomposable $ A$-modules by the roots of the associated quadratic form.

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