Quaternion homology of Banach space (Q2724895)

This paper is concerned with quaternion Banach spaces and their homology. The authors provide the relation between the quaternion and the dihedral homology for a unital involutive Banach algebra.NEWLINENEWLINENEWLINEThe authors define the generalized quaternion group and prove some of its properties, then they define the quaternion Banach space as a family of Banach spaces with some specific linear maps. The continuous quaternion homology is then introduced and a proposition is stated which relates it to the dihedral homology by means of the existence of a bicomplex with \(h\)-periodic rows. The result is extended immediately to the quaternion cohomology for a unital Banach algebra with an involution.