The geometry of uniserial representations of algebras. II: Alternate viewpoints and uniqueness. (English) Zbl 0982.16010
Let \(\Gamma\) be a quiver, and let \(\Lambda=K\Gamma/I\), where \(I\) is an admissible ideal in the path algebra \(K\Gamma\), and \(K\) is an algebraically closed field. The aim of the authors is to prove the invariance up to birational equivalence of the uniserial varieties under a change of coordinatization of \(\Lambda\). They also prove that the natural maps from the uniserial varieties to the set of isomorphism types of uniserial \(\Lambda\)-modules have closed fibres [B. Huisgen-Zimmermann, Part I, J. Pure Appl. Algebra 127, No. 1, 39-72 (1998; Zbl 0951.16005)].
Reviewer: Aleksandr G.Aleksandrov (Moskva)
MSC:
| 16G10 | Representations of associative Artinian rings |
| 16G20 | Representations of quivers and partially ordered sets |
| 16G60 | Representation type (finite, tame, wild, etc.) of associative algebras |
Keywords:
finite dimensional algebras; quivers; uniserial modules; representations; Grassmannians; hereditary algebras; unipotent groups; semisimple modulesCitations:
Zbl 0951.16005References:
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