... q1T
Star complex conjugates A, B, C, D
Bar is product of T and Star
Norm(q) = qTq can be complex, even zero
q in group H1 iff q qT = qT q = 1
4-vector X=t + i*x*I +i*y*J + i*z*K
XPRIME = q X Bar(q) for q in H1
Form with real scalar, imaginary spatial is preserved
Bar(X) = X
Bar(XPRRIME )= XPRIME
Norm(XPRIME) = Norm(X) = t*t - x*x - y*y - z*z
q=cos(theta/2)+K*sin(theta/2) rotates by theta about z
q=cosh(alpha/2)+i*I*sinh(alpha/2) boosts by alpha along x