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

• Date: 2016
• Main Authors: Bondarenko, Vitaliy M., Tertychna, Olena M., Zubaruk, Olesya V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: potent operator; quiver; Krull-Schmidt category; functor; canonical form; tame type; wild type; Dynkin graph; extended Dynkin graph; 15A21; 16G20; 16G60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/170
• Journal Title: Algebra and Discrete Mathematics

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 f...