Subrepresentations of Kronecker representations

Yang Han

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arXiv · math/0403088

Subrepresentations of Kronecker representations

Yang Han

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Abstract

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of their Kronecker invariants. The problem is reduced to a numerical criterion for a Kronecker representation to be a subrepresentation of another Kronecker representation in terms of their Kronecker invariants. The key to the problem is the calculation of ranks of matrices over polynomial rings. For this, a generalization and specialization approach is introduced. This approach is applied to provide a numerical criterion for a preprojective (resp. regular, preinjective) Kronecker representation to be a subrepresentation of another preprojective (resp. regular, preinjective) Kronecker representation in terms of their Kronecker invariants.

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BibTeX RIS

Yang Han. 2005-04-18. Subrepresentations of Kronecker representations. https://arxiv.org/abs/math/0403088

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