On the metric hypercomplex group alternative-elastic algebras for n mod 8 = 0
Abstract
In this article the hypercomplex orthogonal (homogenous) algebra definition is made. It is shown that 1. the hypercomplex orthogonal algebra is the metric hypercomplex group alternative-elastic algebra for n mod 8 = 0 (the non-alternative and non-normalized, but the weakly alternative and weakly normalized for n>8; the alternative and normalized for the oktonion algebra); 2. the hypercomplex orthogonal algebra is generated by a symmetric (0,2)-spinor; 3. the hypercomplex orthogonal homogeneous algebra is generated by the identity algebra, generating algebra and orthogonal transformations; 4. the metric hypercomplex Cayley-Dickson algebra is the hypercomplex special orthogonal homogeneous algebra for n=2k,n>=8. The hypercomplex Cayley-Dickson algebra generator in an explicit form is calculated. Technical realization (Delphi) of the canonical sedenion algebra for n=16 is given according to the point 2-3.