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ON REAL ALGEBRAS ADMITTING REFLECTIONS WHICH COMMUTE
Keywords:
division algebra, algebra isotopy, derivation, reflecionDOI:
https://doi.org/10.17654/0972555524012Abstract
We study real algebras admitting reflections which commute. In dimension two, we show that two commuting reflections coincide. We specify it in the two and four-dimensional real algebras, and characterize two-dimensional real division algebras, and four-dimensional unitary real division algebras at third power-associative having two reflections that commute. In eight-dimensional case, we give an example of an algebra whose group of automorphisms contains a subgroup isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_2$.
Received: November 16, 2023
Accepted: January 19, 2024
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