On a hidden supersymmetry of cosmological billiards
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929499276312576 |
|---|---|
| author | Leites, Dimitry Lozhechnyk, Oleksandr |
| author_facet | Leites, Dimitry Lozhechnyk, Oleksandr |
| contents | The hyperbolic Lie algebras with symmetrizable Cartan matrix are classified, there are 142 of them some of which can be ``superized'' to an almost affine Lie superalgebra. We list all 97 pairs (a hyperbolic Lie algebra $H$, its superized almost affine Lie superalgebra $S(H)$). Several (18 of the total 66) superizable hyperbolic Lie algebras have multiple superizations. The tracks of cosmological billiards corresponding to both terms of these pairs ($H\leftrightarrow S(H)$) are the same since the Weyl chambers of $H$ and of $S(H)$ differ only by a~scale.
We also classified ``superizations'' of hyperbolic Lie algebras with non-symmetrizable Cartan matrix. No interpretations of these Lie (super)algebras are known to us. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_04192 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a hidden supersymmetry of cosmological billiards Leites, Dimitry Lozhechnyk, Oleksandr Mathematical Physics General Relativity and Quantum Cosmology Representation Theory 17B50, 83E50 (Primary) 17B20, 83F05 (Secondary) The hyperbolic Lie algebras with symmetrizable Cartan matrix are classified, there are 142 of them some of which can be ``superized'' to an almost affine Lie superalgebra. We list all 97 pairs (a hyperbolic Lie algebra $H$, its superized almost affine Lie superalgebra $S(H)$). Several (18 of the total 66) superizable hyperbolic Lie algebras have multiple superizations. The tracks of cosmological billiards corresponding to both terms of these pairs ($H\leftrightarrow S(H)$) are the same since the Weyl chambers of $H$ and of $S(H)$ differ only by a~scale. We also classified ``superizations'' of hyperbolic Lie algebras with non-symmetrizable Cartan matrix. No interpretations of these Lie (super)algebras are known to us. |
| title | On a hidden supersymmetry of cosmological billiards |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Representation Theory 17B50, 83E50 (Primary) 17B20, 83F05 (Secondary) |
| url | https://arxiv.org/abs/2102.04192 |