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arXiv · 2607.19513

Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals

Mikhail Borovoi·Willem A. de Graaf·Robert M. Guralnick
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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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Mikhail Borovoi, Willem A. de Graaf, Robert M. Guralnick. 2026-07-21. Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals. https://arxiv.org/abs/2607.19513

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