Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910568499118080 |
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| author | Ivanova, N. M. Pallikaros, C. A. |
| author_facet | Ivanova, N. M. Pallikaros, C. A. |
| contents | We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and Pallikaros C.A., Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras, {\it Advances in Group Theory and Applications}, 18 (2024), 41-79], for some of the arguments in the present article we needed to develop alternative techniques which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the results obtained, corresponding to whether the characteristic of the field is 2 or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09771 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field Ivanova, N. M. Pallikaros, C. A. Rings and Algebras 14R20, 14D06 We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and Pallikaros C.A., Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras, {\it Advances in Group Theory and Applications}, 18 (2024), 41-79], for some of the arguments in the present article we needed to develop alternative techniques which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the results obtained, corresponding to whether the characteristic of the field is 2 or not. |
| title | Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field |
| topic | Rings and Algebras 14R20, 14D06 |
| url | https://arxiv.org/abs/2312.09771 |