From Quaternions to Pentarnions I: Algebra, geometry, and a spin model

Alireza Poshtkohi, Susanne Pumpluen

We introduce a family of five-dimensional non-flexible quadratic real algebras $\{{\mathcal{A}}_{\gamma }{\}}_{0\le \gamma \le 1}$ with canonical basis $1,i,j,k,\ell$, in which $\gamma$ changes the multip…