Extending the theory of linearization of a quadratic transformation in genetic algebra (Q1104400)

If a genetic algebra is regarded as a vector space then the mapping \(A\to^{T}A^ 2\) is, of course, not linear. However by a special trick which involves enlarging the vector space, Victor Abraham has developed a technique (initiated by Holgate) for obtaining a linear mapping which is induced by T. In general the dimension is very high. In this paper the technique is generalized to cases where some of the multiplication coefficients \(\lambda_{ijk}\) are 0 in such a way as to obtain a much smaller dimension for the appropriate vector space.