Quaternionic vector space

In mathematics, a left (or right) quaternionic vector space is a left (or right) H-module where H is the (non-commutative) division ring of quaternions.

The space Hn of n-tuples of quaternions is both a left and right H-module using the componentwise left and right multiplication:

for quaternions q and q1, q2, ... qn.

Since H is a division algebra, every finitely generated (left or right) H-module has a basis, and hence is isomorphic to Hn for some n.

See also edit

References edit

  • Harvey, F. Reese (1990). Spinors and Calibrations. San Diego: Academic Press. ISBN 0-12-329650-1.