Combinatorial aspects of extensions of Kronecker modules

Szántó, Csaba (2014) Combinatorial aspects of extensions of Kronecker modules. Journal of Pure and Applied Algebra. ISSN 0022-4049 (Submitted)

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Abstract

Let $kK$ be the path algebra of the Kronecker quiver and consider the category $\Mod kK$ of finite dimensional right modules over $kK$ (called Kronecker modules). We prove that extensions of Kronecker modules are field independent up to Segre classes, so they can be described purely combinatorially. We use in the proof explicit descriptions of particular extensions and a variant of the well known Green formula for Ringel-Hall numbers, valid over arbitrary fields. We end the paper with some results on extensions of preinjective Kronecker modules, involving the dominance ordering from partition combinatorics and its various generalizations.

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