The **split-quaternions** are an algebra over the real numbers. Every split quaternion $q$ may be represented as

$q = a_0 + a_1 i + a_2 j + a_3k$

where the basis elements satisfy the following products:

$\times$ | i | j | k |
---|---|---|---|

i | -1 | k | -j |

j | -k | +1 | -i |

k | j | i | +1 |

and conjugation $t^* = a_0 - a_1 i - a_2 j - a_3k$.

These are closely related to the quaternions, as the generators satisfy similarly-looking relations. They are obtained from the split-complex numbers through the generalization of the Cayley-Dickson construction.

See also

- Wikipedia,
*Split-quaternion*

On projective spaces over split-quaternions:

- Konrad Voelkel,
*Motivic cell structures for projective spaces over split quaternions*, 2016 (freidok:11448, pdf)

Last revised on November 3, 2023 at 05:16:33. See the history of this page for a list of all contributions to it.