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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21279 |
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| _version_ | 1866910114491924480 |
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| author | Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea |
| author_facet | Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea |
| contents | In 1981 Antonyan classified the orbits of SL$(8,\mathbb{C})$ on $\bigwedge^4 \mathbb{C}^8$. This is an example of a $θ$-group action as introduced and studied by Vinberg. The orbits of a $θ$-group are divided into three classes: nilpotent, semisimple and mixed. We consider the action of SL$(8,\mathbb{R})$ on $\bigwedge^4 \mathbb{R}^8$ and classify the nilpotent and semisimple orbits as well as the Cartan subspaces. The semisimple orbits are divided into 1441 parametrized classes. Due to this high number a classification of the mixed orbits does not seem feasible. Our methods are based on Galois cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of nilpotent and semisimple fourvectors of a real eight-dimensional space Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea Representation Theory Rings and Algebras In 1981 Antonyan classified the orbits of SL$(8,\mathbb{C})$ on $\bigwedge^4 \mathbb{C}^8$. This is an example of a $θ$-group action as introduced and studied by Vinberg. The orbits of a $θ$-group are divided into three classes: nilpotent, semisimple and mixed. We consider the action of SL$(8,\mathbb{R})$ on $\bigwedge^4 \mathbb{R}^8$ and classify the nilpotent and semisimple orbits as well as the Cartan subspaces. The semisimple orbits are divided into 1441 parametrized classes. Due to this high number a classification of the mixed orbits does not seem feasible. Our methods are based on Galois cohomology. |
| title | Classification of nilpotent and semisimple fourvectors of a real eight-dimensional space |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2511.21279 |