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The geometry of uniserial representations of algebras II. Alternate viewpoints and uniqueness

✍ Scribed by Klaus Bongartz; Birge Huisgen-Zimmermann

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 121 KB
Volume: 157
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00031-1

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✦ Synopsis

We provide two alternate settings for the family of varieties, introduced in Huisgen-Zimmermann (J. Pure Appl. Algebra 127 (1998) 39 -72), which model the uniserial representations of a ÿnite-dimensional algebra. The ÿrst is a quasi-projective subvariety of a Grassmannian containing the members of the mentioned family as a principal a ne open cover; among other beneÿts, one derives invariance from this intrinsic description of the 'uniserial varieties'. The second viewpoint re-interprets these varieties as locally closed subsets of the traditional module varieties; in particular, it exhibits closedness of the ÿbres of the canonical maps from the uniserial varieties to the uniserial representations.

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