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

Vitaliy M. Bondarenko, Olena M. Tertychna, Olesya V. Zubaruk

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

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