In mathematics, a left (or right) quaternionic vector space is a left (or right) -module where is the division ring of quaternions. One must distinguish between left and right quaternionic vector spaces since is non-commutative. Further, is not a field, so quaternionic vector spaces are not vector spaces, but merely modules.
The space is both a left and right quaternionic vector space using componentwise multiplication. Namely, for and ,
Since is a division algebra, every finitely generated (left or right) -module has a basis, and hence is isomorphic to for some .
See also
editReferences
edit- Harvey, F. Reese (1990). Spinors and Calibrations. San Diego: Academic Press. ISBN 0-12-329650-1.