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May 23, 2017 at 11:23 comment added user21230 I prefer the $\cdot ^S$ formula as well :) I will not reveal whether I am right or left-handed here :) Note that if we assume that quaternion commutes with extra element $\iota$ then we can obtain $\mathbb C\otimes \mathbb H$ = $M_2\mathbb C$, namely formula is:$ (a,b)\cdot (c,d)=(ac-bd, ad+bc) \textrm{ for } a,b,c,d\in \mathbb H $
Mar 11, 2017 at 12:21 history answered Gro-Tsen CC BY-SA 3.0