Matrix problems and noexpand representations of algebras
This paper is devoted to the theory of matrix problems, a new branch of modern algebra created and developed to a large extent by the Kyiv algebraic school. It originated from the questions of the theory of representations, but now has proved its efficiency in many areas, such as algebraic geometry,...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/502 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| _version_ | 1872552999692271616 |
|---|---|
| author | Drozd, Yuriy Дрозд, Юрій |
| author_facet | Drozd, Yuriy Дрозд, Юрій |
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"author": "Yuriy Drozd",
"institution": "Institute of mathematics NAS of Ukraine, Kyiv"
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| author_sort | Drozd, Yuriy |
| baseUrl_str | https://trim.imath.kiev.ua/index.php/trim/oai |
| collection | OJS |
| datestamp_date | 2022-01-17T21:33:15Z |
| description | This paper is devoted to the theory of matrix problems, a new branch of modern algebra created and developed to a large extent by the Kyiv algebraic school. It originated from the questions of the theory of representations, but now has proved its efficiency in many areas, such as algebraic geometry, algebraic topology, linear algebra, theory of groups etc.
Certainly, I could not embraced all achievements or even all directions of investigation, so their choice in the paper is rather subjective. Moreover, I only consider the <<classical results>>, not involving the new investigations and applications to algebraic geometry and algebraic topology (see surveys~\cite{cm,top}). |
| first_indexed | 2026-08-04T01:08:21Z |
| format | Article |
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| id | oai:trim.imath.kiev.ua:article-502 |
| institution | Transactions of Institute of Mathematics of NAS of Ukraine |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-08-04T01:08:21Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
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| resource_txt_mv | |
| spelling | oai:trim.imath.kiev.ua:article-5022022-01-17T21:33:15Z Matrix problems and noexpand representations of algebras Drozd, Yuriy Дрозд, Юрій This paper is devoted to the theory of matrix problems, a new branch of modern algebra created and developed to a large extent by the Kyiv algebraic school. It originated from the questions of the theory of representations, but now has proved its efficiency in many areas, such as algebraic geometry, algebraic topology, linear algebra, theory of groups etc. Certainly, I could not embraced all achievements or even all directions of investigation, so their choice in the paper is rather subjective. Moreover, I only consider the <<classical results>>, not involving the new investigations and applications to algebraic geometry and algebraic topology (see surveys~\cite{cm,top}). Ця стаття присвячена теорії матричних задач, новій галузі сучасної алгебри, яка була створена й розвинена значною мірою Київською алгебричною школою. Вона виникла з проблем теорії зображень, але зараз вже довела свою ефективність у багатьох галузях, таких як алгебрична геометрія, алгебрична топологія, лінійна алгебра, теорія груп, тощо.  Звичайно, я не міг охопити всі досягнення або хоча б усі напрямки досліджень, тож їхній вибір у статті досить суб'єктивний. Більш того, я обмежився лише <<класичними>> результатами, не торкаючись новітніх досліджень і застосувань до алгебричної геометрії та алгебричної топології (дивись огляди~\cite{cm,top}). Інститут математики НАН України 2022-01-17 Article Article https://trim.imath.kiev.ua/index.php/trim/article/view/502 Transactions of Institute of Mathematics, the NAS of Ukraine; Vol. 17 No. 2 (2020): Modern problems of mathematics and its applications, I; 57-81 Сборник Трудов Института математики НАН Украины; Том 17 № 2 (2020): Сучасні проблеми математики та її застосувань, I; 57-81 Збірник Праць Інституту математики НАН України; Том 17 № 2 (2020): Сучасні проблеми математики та її застосувань, I; 57-81 3083-7529 1815-2910 en Авторське право (c) 2022 Юрій Дрозд http://creativecommons.org/licenses/by/4.0 |
| spellingShingle | Drozd, Yuriy Дрозд, Юрій Matrix problems and noexpand representations of algebras |
| title | Matrix problems and noexpand representations of algebras |
| title_full | Matrix problems and noexpand representations of algebras |
| title_fullStr | Matrix problems and noexpand representations of algebras |
| title_full_unstemmed | Matrix problems and noexpand representations of algebras |
| title_short | Matrix problems and noexpand representations of algebras |
| title_sort | matrix problems and noexpand representations of algebras |
| url | https://trim.imath.kiev.ua/index.php/trim/article/view/502 |
| work_keys_str_mv | AT drozdyuriy matrixproblemsandnoexpandrepresentationsofalgebras AT drozdûríj matrixproblemsandnoexpandrepresentationsofalgebras |