Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field
UDC 512.5+514 We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension three over an algebraically closed field.  As compared with the discussion in [N. M. Ivanova, C. A. Pallikaros,  Adv. Group Theory and...
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| Дата: | 2025 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
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Institute of Mathematics, NAS of Ukraine
2025
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7987 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512838352633856 |
|---|---|
| author | Ivanova, N. M. Pallikaros, C. A. Ivanova, N. M. Pallikaros, C. A. |
| author_facet | Ivanova, N. M. Pallikaros, C. A. Ivanova, N. M. Pallikaros, C. A. |
| author_sort | Ivanova, N. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-08-09T14:51:16Z |
| description | UDC 512.5+514
We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension three over an algebraically closed field.  As compared with the discussion in [N. M. Ivanova, C. A. Pallikaros,  Adv. Group Theory and Appl., 18, 41-79 (2024)], for some arguments in the present article, it is necessary to develop alternative techniques, which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the  obtained results corresponding to the cases where the characteristic of the field is $2$ or not. |
| doi_str_mv | 10.3842/umzh.v76i11.7987 |
| first_indexed | 2026-03-24T03:35:09Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7987 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:35:09Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-79872025-08-09T14:51:16Z Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field Ivanova, N. M. Pallikaros, C. A. Ivanova, N. M. Pallikaros, C. A. degeneration; orbit closure; nilpotent associative algebra UDC 512.5+514 We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension three over an algebraically closed field.  As compared with the discussion in [N. M. Ivanova, C. A. Pallikaros,  Adv. Group Theory and Appl., 18, 41-79 (2024)], for some arguments in the present article, it is necessary to develop alternative techniques, which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the  obtained results corresponding to the cases where the characteristic of the field is $2$ or not. УДК 512.5+514 Виродження 3-вимірних нільпотентних асоціативних алгебр над алгебраїчно замкненим полем Визначено повну картину виродження всередині многовиду нільпотентних асоціативних алгебр розмірності три над алгебраїчно замкненим полем. Порівняно з дискусією в [N. M. Ivanova, C. A. Pallikaros,  Adv. Group Theory and Appl., 18, 41-79 (2024)], для деяких аргументів, наведених у цій статті, потрібно було розвинути альтернативні методи, справедливі над довільним алгебраїчно замкненим полем. Існує дихотомія випадків щодо отриманих результатів залежно від того, чи  характеристика поля дорівнює $2,$ чи ні. Institute of Mathematics, NAS of Ukraine 2025-08-06 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7987 10.3842/umzh.v76i11.7987 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 11 (2024); 1610 - 1620 Український математичний журнал; Том 76 № 11 (2024); 1610 - 1620 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7987/10280 Copyright (c) 2024 Christakis Pallikaros |
| spellingShingle | Ivanova, N. M. Pallikaros, C. A. Ivanova, N. M. Pallikaros, C. A. Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_alt | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_full | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_fullStr | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_full_unstemmed | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_short | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| title_sort | degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| topic_facet | degeneration orbit closure nilpotent associative algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7987 |
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