Опис алгебри Ауслендера єдиної некомутативної напівгрупи третього порядку з ненульовим нільпотентним елементом
One way to describe the category of representations over a field of an algebraic object that has a finite number of equivalence classes of indecomposable objects is to compute its Auslander algebra as the algebra of endomorphisms of a direct sum of all indecomposable representations (with one repres...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
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Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2026
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| Subjects: | |
| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/3653 |
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| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Summary: | One way to describe the category of representations over a field of an algebraic object that has a finite number of equivalence classes of indecomposable objects is to compute its Auslander algebra as the algebra of endomorphisms of a direct sum of all indecomposable representations (with one representative from each class). The paper describes the Auslander algebra of the third order semigroup with the elements 0, b, c and the defining relations b2=0, c2=c, bc=0, cb=b, the unique, up to isomorphism, non-commutative semigroup of order three which contains a non-zero nilpotent element. The case of commutative third order semigroups were considered by the authors earlier. Cite as: V. M. Bondarenko, M. V. Styopochkina, “Classification of the Auslander algebras of the unique non-commutative third order semigroup with a non-zero nilpotent element,” Прикл. проблеми механіки і математики, Issue 23, 5–10 (2025) (in Ukrainian), https://doi.org/10.15407/apmm2025.23.5-10 |
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| DOI: | 10.15407/3653 |