Nilpotent symplectic alternating algebras II
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916327251247104 |
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| author | Sorkatti, Layla Traustason, Gunnar |
| author_facet | Sorkatti, Layla Traustason, Gunnar |
| contents | In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension $10$ over any field. It is known that symplectic alternating algebras over $\mbox{GF}(3)$ correspond to a special rich class $\mathcal{C}$ of $2$-Engel $3$-groups of exponent $27$ and under this correspondence we will see that the nilpotent algebras correspond to a subclass of $\mathcal{C}$ that are those groups in $\mathcal{C}$ that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of $p$-groups where $p$ is an arbitrary prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nilpotent symplectic alternating algebras II Sorkatti, Layla Traustason, Gunnar Rings and Algebras 17D99, 20F45, 20D15 In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension $10$ over any field. It is known that symplectic alternating algebras over $\mbox{GF}(3)$ correspond to a special rich class $\mathcal{C}$ of $2$-Engel $3$-groups of exponent $27$ and under this correspondence we will see that the nilpotent algebras correspond to a subclass of $\mathcal{C}$ that are those groups in $\mathcal{C}$ that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of $p$-groups where $p$ is an arbitrary prime. |
| title | Nilpotent symplectic alternating algebras II |
| topic | Rings and Algebras 17D99, 20F45, 20D15 |
| url | https://arxiv.org/abs/2404.11038 |