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arXiv · 2208.14832

Anti-commutative algebras and their groups of automorphisms

Ágota Figula·Péter T. Nagy
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Abstract

We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie algebras, and hence can be considered as the closest relatives of binary Lie algebras. These algebras are extensions of $\mathbb K$ by the 3-dimensional nilpotent Lie algebra and at the same time extensions of a two-dimensional Lie algebra by a two-dimensional abelian algebra. We describe their groups of automorphisms as extensions of a subgroup of the group of automorphisms of the three-dimensional nilpotent Lie algebra by $\mathbb K$.

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Ágota Figula, Péter T. Nagy. 2022-08-31. Anti-commutative algebras and their groups of automorphisms. https://arxiv.org/abs/2208.14832

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