split-quaternions

[RobinHankin]

The split-quaternions or coquaternions https://en.wikipedia.org/wiki/Split-quaternion have a nice Clifford representation:

suppressMessages(library("clifford"))
signature(2,1)
options(maxdim=3)
i <- -e(c(1,2))
j <- -e(c(1,3))
k <- -e(c(2,3))

c(i^2 ==-1, j^2 == 1, k^2==1, i*j*k == 1)
#> [1] TRUE TRUE TRUE TRUE
c(i*j == k, j*i == -k,  j*k == -i, k*j == i,  k*i == j,  i*k == -j)
#> [1] TRUE TRUE TRUE TRUE TRUE TRUE

^{Created on 2023-08-22 with reprex v2.0.2}