Shoot Koebisu

Determinant Factorization of Left Multiplication in the 32 Dimensional Cayley Dickson Algebra

We study the determinant of left multiplication in the 32-dimensional Cayley-Dickson algebra $A_5$. For $x \in A_5$, let $L_x$ denote left multiplication and let $N(x)=|x|^2$. Using the fourfold multiplicity of the eigenspaces of $L_{x^*}L_x$ and Newton identities applied to its trace invariants, we construct a homogen...