Geodesic
On classification of pairs of potent linear operators with the simplest annihilation condition
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 18-23

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We study the problem of classifying the pairs of linear operators $\mathcal{A}, \mathcal{B}$ (acting on the same vector space), when the both operators are potent and $\mathcal{A}\mathcal{B}=0$. We describe the finite, tame and wild cases and classify the indecomposable pairs of operators in the first two of them.
Keywords: potent operator, quiver, Krull-Schmidt category, functor, canonical form, wild type, extended Dynkin graph.
Mots-clés : tame type, Dynkin graph 
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     title = {On classification of pairs of potent linear operators with the simplest annihilation condition},
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Vitaliy M. Bondarenko; Olena M. Tertychna; Olesya V. Zubaruk. On classification of pairs of potent linear operators with the simplest annihilation condition. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 18-23. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a2/