Subrepresentations of Kronecker Representations
نویسنده
چکیده
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.
منابع مشابه
Generalities on representations of finite groups
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/03 generalities finite.pdf] 1. Subrepresentations, complete reducibility, unitarization 2. Dual/contragredient representations 3. Regular and biregular representations L(G) 4. Schur’s lemma 5. Central characters of irreducibles 6. Tensor products of repres...
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تاریخ انتشار 2004