ON REAL ALGEBRAS ADMITTING REFLECTIONS WHICH COMMUTE
André Souleye Diabang, Mankagna Albert Diompy, Alhousseynou Ba · JP Journal of Algebra Number Theory and Applications · 2024
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, 2023Accepted: January 19, 2024