Involutions of complexified quaternions and split quaternions (Q353027)

The paper deals with involutions and anti-involutions of the algebra \(\mathbb H\) of Hamilton quaternions, the so called split quaternion algebra \(M_2(\mathbb R)\), and the algebra \(\mathbb C\otimes_R\mathbb H\cong M_2(\mathbb C)\) of biquaternions. The \textit{M.-A. Knus} et al. [Book of Involutions. Providence, RI: AMS (1998; Zbl 0955.16001)] is praised in the beginning. As ``the formal definition of an involution is not easy to find'', Hamilton's system of axioms for an involution is reproduced [Trans. R. Ir. Acad. (1848)]. Geometric interpretations for involutions and anti-involutions in the different cases are given. In this section (page 295--298), the paper contains 11 theorems.