Incoming links: Quaternion
A vector field with a bilinear map into itself, which we can also call a "vector product".
Note that the vector product does not have to be neither associative nor commutative.
Examples: en.wikipedia.org/w/index.php?title=Algebra_over_a_field&oldid=1035146107#Motivating_examples
- complex numbers, i.e. with complex number multiplication
- with the cross product
- quaternions, i.e. with the quaternion multiplication
Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.
Notably, the octonions are not associative.
Unlike the quaternions, it is non-associative.