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Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals
Abstract
Following an idea of Demarche and using computer calculations of the authors and ideas of the LLM Claude Fable 5, we construct an explicit 10-dimensional complex two-step nilpotent Lie algebra that is isomorphic to its complex conjugate but cannot be defined over the field of real numbers R.
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BibTeX
@misc{borovoi2026constructing,
title = {{Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals}},
author = {Mikhail Borovoi and Willem A. de Graaf and Robert M. Guralnick},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19513},
eprint = {2607.19513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19513},
}
RIS
TY - UNPB
TI - Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals
AU - Mikhail Borovoi
AU - Willem A. de Graaf
AU - Robert M. Guralnick
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2607.19513
UR - https://arxiv.org/abs/2607.19513
AB - Following an idea of Demarche and using computer calculations of the authors and ideas of the LLM Claude Fable 5, we construct an explicit 10-dimensional complex two-step nilpotent Lie algebra that is isomorphic to its complex conjugate but cannot be defined over the field of real numbers R.
ER -