Abstract
For any truncated path algebra of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties of the -modules with fixed dimension vector . In this situation, the components of are always among the closures , where traces the semisimple sequences with dimension vector , and hence the key to the classification problem lies in a characterization of these closures.
Our first result concerning closures actually addresses arbitrary basic finite-dimensional algebras over an algebraically closed field. In the general case, it corners the closures by means of module filtrations “governed by ”; when is truncated, it pins down the completely.
The analysis of the varieties leads to a novel upper semicontinuous module invariant which provides an effective tool towards the detection of components of in general. It detects all components when is truncated.
Citation
Kenneth R. Goodearl. Birge Huisgen-Zimmermann. "Closures in varieties of representations and irreducible components." Algebra Number Theory 12 (2) 379 - 410, 2018. https://doi.org/10.2140/ant.2018.12.379
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