1202.0941 (K. V. Andreev)

On the metric hypercomplex group alternative-elastic algebras for n mod
8 = 0    [PDF]

K. V. Andreev

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.

View original: http://arxiv.org/abs/1202.0941