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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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7987 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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| DOI: | 10.3842/umzh.v76i11.7987 |