It is possible make something like complexification of a real vector space using quaternions? If yes, it's similar to complex case or there are considerable differences? Has been studied a quaternion analysis? thank you!
2026-04-04 08:09:21.1775290161
Some questions about quaternions.
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It is no longer a vector space, but a module over a division algebra. Complexification is generalized by "extension of scalars," where an $R$-module (resp. $R$-algebra) $A$ is turned into an $S$-module (resp. $S$-algebra) via tensoring, $A_S\cong S\otimes_R A$. (Here $S$ is a ring containing $R$ as a subring.)