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Algebra and Discrete Mathematics, 2016, Volume 21, Issue 1, Pages 18–23 (Mi adm551)  
RESEARCH ARTICLE

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

Vitaliy M. Bondarenkoa, Olena M. Tertychnab, Olesya V. Zubarukc

a 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
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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.
Received: 18.02.2016
Bibliographic databases:
Document Type: Article
MSC: 15A21, 16G20, 16G60
Language: English
Citation: Vitaliy M. Bondarenko, Olena M. Tertychna, Olesya V. Zubaruk, “On classification of pairs of potent linear operators with the simplest annihilation condition”, Algebra Discrete Math., 21:1 (2016), 18–23
Citation in format AMSBIB
\Bibitem{BonTerZub16}
\by Vitaliy~M.~Bondarenko, Olena~M.~Tertychna, Olesya~V.~Zubaruk
\paper On classification of pairs of potent linear operators with the simplest annihilation condition
\jour Algebra Discrete Math.
\yr 2016
\vol 21
\issue 1
\pages 18--23
\mathnet{http://mi.mathnet.ru/adm551}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3537482}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000382847600003}
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