A note on complex Lie Algebras isomorphic to their conjugate
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911576068456448 |
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| author | Demarche, Cyril |
| author_facet | Demarche, Cyril |
| contents | A real Lie algebra defines by extension of scalars a complex Lie algebra that is isomorphic to its Galois conjugate. In this paper, we are interested in the converse property: given a complex Lie algebra that is isomorphic to its conjugate, is it defined over the real numbers? We prove the existence of a $10$-dimensional nilpotent complex Lie algebra for which the answer is negative, disproving a recent conjecture by Deré. In addition, we compute the generic obstruction to this descent problem in terms of Brauer groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06979 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on complex Lie Algebras isomorphic to their conjugate Demarche, Cyril Algebraic Geometry Number Theory Representation Theory A real Lie algebra defines by extension of scalars a complex Lie algebra that is isomorphic to its Galois conjugate. In this paper, we are interested in the converse property: given a complex Lie algebra that is isomorphic to its conjugate, is it defined over the real numbers? We prove the existence of a $10$-dimensional nilpotent complex Lie algebra for which the answer is negative, disproving a recent conjecture by Deré. In addition, we compute the generic obstruction to this descent problem in terms of Brauer groups. |
| title | A note on complex Lie Algebras isomorphic to their conjugate |
| topic | Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2604.06979 |