Right, but while the Cayley-Dickson construction mostly provides novelties (though I remember reading something about octonions and string theory[1]), Clifford

Right, but while the Cayley-Dickson construction mostly provides novelties (though I remember reading something about octonions and string theory[1]), Clifford algebras are derived differently; they are isomorphic to complex numbers and quaternions for two and three base vectors respectively, but they produce something else after quaternion. This "something different" can be used to represent, you guessed it, reflections and rotations in a 4D space. Because they are not obtained from the Cayley-Dickson construction they are not division algebras, however. [1] https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ https://www.quantamagazine.org/the-octonion-math-that-could-...