PreprintCC BY-SA 4.0arXiv
A 9-dimensional nilpotent Lie algebra isomorphic to its complex conjugate admitting no real form
Abstract
We give an explicit example of a 9-dimensional 5-step nilpotent complex Lie algebra, generated by two elements, that is isomorphic to its complex conjugate but has no real form. In contrast to the earlier 10-dimensional examples, our proof is completely elementary and very short.
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BibTeX
@misc{medts20269dimensional,
title = {{A 9-dimensional nilpotent Lie algebra isomorphic to its complex conjugate admitting no real form}},
author = {Tom De Medts},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13707},
eprint = {2610.13707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13707},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A 9-dimensional nilpotent Lie algebra isomorphic to its complex conjugate admitting no real form
AU - Tom De Medts
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13707
UR - https://arxiv.org/abs/2610.13707
AB - We give an explicit example of a 9-dimensional 5-step nilpotent complex Lie algebra, generated by two elements, that is isomorphic to its complex conjugate but has no real form. In contrast to the earlier 10-dimensional examples, our proof is completely elementary and very short.
ER -