Differential geometry and complex analysis, Vol. dedic. H. E. Rauch, 65-73 (1985).
[For the entire collection see Zbl 0561.00010.]
The author gives an introduction to the use of Clifford numbers for the study of Möbius transformations in . Let be a base of and let be the Clifford algebra generated by the rules , , unit element, over . Every vector is invertible with , being the Euclidean norm and for , . The products of vectors different from zero form the Clifford group . Another conjugation ”*” in is generated by reversing the order of the factors in each
The main theorem shows that induces a bijective mapping of onto if and only if belongs to , which means if (i) , (ii) , (iii) , , , . Further theorems in this direction are given, a very interesting and clear paper. The author has found first steps in a paper by K. Th. Vahlen [Math. Ann. 55, 585-593 (1902)].