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arXiv · 2608.23015

Three-dimensional simple real Bol algebras

Giovanni Falcone·Ágota Figula·Emese Kása·Gianmarco Mattana·Péter T. Nagy
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Abstract

In this paper, we provide a complete classification of real three-dimensional simple Bol algebras $(B, [.,.], \langle .,.,. \rangle )$. The main part of the classification concerns the case $[B,B]=B$. In addition, we identify two isomorphism classes with a nonzero binary product, both satisfying $\dim[B,B]=2$, as well as four simple classes of Lie triple systems in which the binary product vanishes.

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Giovanni Falcone, Ágota Figula, Emese Kása, Gianmarco Mattana, Péter T. Nagy. 2026-08-24. Three-dimensional simple real Bol algebras. https://arxiv.org/abs/2608.23015

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