Projects per year
Abstract
We classify states of four rebits, that is, we classify the orbits of the group Gˆ(R)=SL(2,R)^{4} in the space (R^{2})^{⊗4}. This is the real analogon of the wellknown SLOCC operations in quantum information theory. By constructing the Gˆ(R)module (R^{2})^{⊗4} via a Z/2Zgrading of the simple split real Lie algebra of type D_{4}, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017) [26], yielding applications in theoretical physics (extremal black holes in the STU model of N=2,D=4 supergravity, see Ruggeri and Trigiante (2017) [51]). Here we focus on the semisimple and mixed orbits which we classify with recently developed methods based on Galois cohomology, see Borovoi et al. (2021) [8,9]. These orbits are relevant to the classification of nonextremal (or extremal overrotating) and twocenter extremal black hole solutions in the STU model.
Original language  English 

Article number  104610 
Number of pages  31 
Journal  Journal of Geometry and Physics 
Volume  179 
DOIs  
Publication status  Published  Sept 2022 
Keywords
 Galois cohomology
 Graded Lie algebras
 Orbits of real Lie groups
 Rebits
Projects
 1 Finished

Computing with Lie groups and algebras: nilpotent orbits and applications
Dietrich, H. & de Graaf, W. A.
1/04/19 → 31/01/23
Project: Research