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arXiv · 2211.00334

Central extensions of axial algebras

Ivan Kaygorodov·Cándido Martín González·Pilar Páez-Guillán
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Abstract

In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split and that all non-split axial central extensions of dimension $n\leq 4$ over an algebraically closed field of characteristic not $2$ are Jordan. Also, we give a classification of $2$-dimensional axial algebras and describe some important properties of these algebras.

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Ivan Kaygorodov, Cándido Martín González, Pilar Páez-Guillán. 2022-11-01. Central extensions of axial algebras. https://arxiv.org/abs/2211.00334

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