Classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917620223049728 |
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| author | Mukherjee, Snehashis |
| author_facet | Mukherjee, Snehashis |
| contents | In this article the right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ has been classified. We use the connection between nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ and nilpotent pre-Lie algebras of the same order, building on the known relationship between pre-Lie algebras and braces. Leveraging insights from the classification of nilpotent pre-Lie algebras over $\mathbb{F}_p$, we aim to provide a comprehensive classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ Mukherjee, Snehashis Quantum Algebra Group Theory Rings and Algebras In this article the right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ has been classified. We use the connection between nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ and nilpotent pre-Lie algebras of the same order, building on the known relationship between pre-Lie algebras and braces. Leveraging insights from the classification of nilpotent pre-Lie algebras over $\mathbb{F}_p$, we aim to provide a comprehensive classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$. |
| title | Classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ |
| topic | Quantum Algebra Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2403.14975 |