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arXiv · 2309.05237

Axial view on pseudo-composition algebras and train algebras of rank 3

Ilya Gorshkov·Andrey Mamontov·Alexey Staroletov
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Abstract

We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called $\mathcal{PC}(\eta)$-axial algebras, where $\eta$ is an element of the ground field. As a first step towards their classification, we describe $2-$ and $3$-generated subalgebras of such algebras.

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Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov. 2023-09-11. Axial view on pseudo-composition algebras and train algebras of rank 3. https://arxiv.org/abs/2309.05237

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