On the metric hypercomplex group alternative-elastic algebras for n mod   8 = 0
  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=2^k,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. 
K.V. Andreev
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