Hyperbolic quaternion
In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q = a + b i + c j + d k , a , b , c , d ∈ R {\displaystyle q=a+bi+cj+dk,\quad a,b,c,d\in \mathbb {R} \! } where the squares of i, j, and k are +1 and distinct elements of {i, j, k} multiply with the anti-commutative property. The four-dimensional algebra of hyperbolic quaternions incorporates some of the features of the older and larger algebra of biquaternions.