Classification of four-rebit states

We classify states of four rebits, that is, we the orbits group Gˆ(R)=SL(2,R)4 in space (R2)⊗4. This is real analogon well-known SLOCC operations quantum information theory. By constructing Gˆ(R)-module (R2)⊗4 via a Z/2Z-grading simple split Lie algebra type D4, are divided into three groups: semisimple, nilpotent and mixed. The have been classified Dietrich et al. (2017) [26], yielding applications theoretical physics (extremal black holes STU model N=2,D=4 supergravity, see Ruggeri Trigiante [51]). Here focus on semisimple mixed which with recently developed methods based Galois cohomology, Borovoi (2021) [8], [9]. These relevant to classification non-extremal (or extremal over-rotating) two-center hole solutions model.