A 10-dimensional nilpotent complex Lie algebra exists that is isomorphic to its conjugate but not defined over the reals, disproving Deré's conjecture, with the generic obstruction computed in terms of Brauer groups.
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A note on complex Lie Algebras isomorphic to their conjugate
A 10-dimensional nilpotent complex Lie algebra exists that is isomorphic to its conjugate but not defined over the reals, disproving Deré's conjecture, with the generic obstruction computed in terms of Brauer groups.