The geometry of uniserial representations of finite dimensional algebras. III: Finite uniserial type

Huisgen-Zimmermann, Birge

doi:10.1090/S0002-9947-96-01575-9

The geometry of uniserial representations of finite dimensional algebras. III: Finite uniserial type
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by Birge Huisgen-Zimmermann

Trans. Amer. Math. Soc. 348 (1996), 4775-4812

DOI: https://doi.org/10.1090/S0002-9947-96-01575-9

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Abstract:

A description is given of those sequences $\mathbf {S}= (S(0),S(1),\dots ,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors $S(0),\dots , S(l)$. Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series $\mathbf {S}$.

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