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

division algebra, algebra isotopy, derivation, reflecion.

Received: November 16, 2023;  Accepted: January 19, 2024; Published: March 9, 2024

How to cite this article: André Souleye Diabang, Mankagna Albert Diompy and Alhousseynou Ba, On real algebras admitting reflections which commute, JP Journal of Algebra, Number Theory and Applications  63(3) (2024), 209-223. http://dx.doi.org/10.17654/0972555524012

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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