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arXiv · 2404.11038

Nilpotent symplectic alternating algebras II

Layla Sorkatti·Gunnar Traustason
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Abstract

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.

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Layla Sorkatti, Gunnar Traustason. 2024-04-17. Nilpotent symplectic alternating algebras II. https://doi.org/10.1142/s0218196716500454

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