A new eigenspace characterization of split-quaternion involutions

Abstract

It is well known that a general quaternion algebra over a field F of characteristic different from 2 is either a division algebra or is split, which means isomorphic to M-2(F) the algebra of 2 x 2-matrices with entries from F. Since we have characterized in [Lawson J, Kizil E. Characterization of automorphic and anti-automorphic involutions of the quaternions. Linear Multilin Algebra, Published online. 04/2020] automorphic and anti-automorphic involutions of the division algebra of Hamilton's quaternions, we treat in this paper splitquaternions and obtain characterizations of the class of involutions of the algebra of split quaternions both in terms of inner automorphisms and of involution eigenspaces. These descriptions carry over to involutive automorphisms.