Generic representations of wild quivers
Claus Michael Ringel

TL;DR
This paper demonstrates that generic representations of wild connected directed quivers are unions of finite-length regular subrepresentations, revealing structural properties and limitations of certain module classes.
Contribution
It establishes that generic modules are unions of regular subrepresentations and shows the direct limit closure of the preprojective component lacks generic modules.
Findings
Generic representations are unions of finite-length regular subrepresentations.
The direct limit closure of the preprojective component contains no generic modules.
Abstract
We show that any generic representation of a wild connected directed quiver is the union of its subrepresentations of finite length which are regular. As a consequence, we see that the direct limit closure of the preprojective component does not contain any generic module.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis
