The Lie Group S3 in Absolute Valued Structures

Abstract We develop techniques of conjugation, with respect to a certain maximal tori in the Lie group S3, in the framework of absolute valued structures. As a consequence, we give a classification of four-dimensional absolute-valued triple systems attending just to three reals and one quaternion in the nonexceptional case and one more quaternion in the exceptional case. The isomorphism classes among them are also stated.