RESEARCH ARTICLE

On classification of pairs of potent linear operators with the simplest annihilation condition

Vitaliy M. Bondarenko^a, Olena M. Tertychna^b, Olesya V. Zubaruk<sup>c

a</sup> Institute of Mathematics, NAS, Kyiv, Ukraine
^b Vadim Hetman Kyiv National Economic University, Kiev, Ukraine
^c Kyiv National Taras Shevchenko University, Volodymyrska str., 64, 01033 Kyiv, Ukraine

Abstract: 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, tame type, wild type, Dynkin graph, extended Dynkin graph.

MSC: 15A21, 16G20, 16G60

Received: 18.02.2016

Language: English

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