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Well, Papa, can you multiply triplets?
Sophie Morier-Genoud1, Valentin Ovsienko2

We show that the classical algebra of quaternions is a commutative $\Z_2\times\Z_2\times\Z_2$-graded algebra. A similar interpretation of the algebra of octonions is impossible.
1:  IMJ - Institut de Mathématiques de Jussieu
2:  ICJ - Institut Camille Jordan
quaternions – graded commutative algebra