Hypercomplex numbers in the work of Caspar Wessel and Hermann Günther Grassmann: Are there any singularities? (Q2762233)

The article describes the contribution of C. Wessel and H. G. Grassmann to the theory of hypercomplex numbers. Wessel presented his ideas in his paper about the geometrical representation of complex numbers when he tried to extend these magnitudes and studied numbers which were formed by three basic units. Grassmann's investigations on hypercomplex numbers can be considered as a formal continuation of Wessel's ideas. In his `Ausdehnungslehre' of 1844 (see Zbl 0923.01019 for an English translation) Grassmann developed first steps to a theory of \(n\)-dimensional vector spaces and of hypercomplex numbers. These results as well as his thorough investigations on various definitions of the product of hypercomplex numbers are discussed in detail. Finally a comparison of Wessel's and Grassmann's work is given.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00008].