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 (R2)⊗4. This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the Gˆ(R)-module (R2)⊗4 via a Z/2Z-grading of the simple split real Lie algebra of type D4, 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 non-extremal (or extremal over-rotating) and two-center extremal black hole solutions in the STU model.
Original language | English |
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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
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Computing with Lie groups and algebras: nilpotent orbits and applications
Dietrich, H. & de Graaf, W. A.
1/04/19 → 1/08/23
Project: Research