On the nonrationality of rigid Lie algebras

Bermudez, J.; Goze, M.

doi:10.1090/S0002-9939-99-04824-8

On the nonrationality of rigid Lie algebras
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by J. M. Ancochea Bermudez and M. Goze PDF

Proc. Amer. Math. Soc. 127 (1999), 2611-2618 Request permission

Abstract:

In his thesis, Carles made the following conjecture: Every rigid Lie algebra is defined on the field $Q$. This was quite an interesting question because a positive answer would give a nice explanation of the fact that simple Lie algebras are defined over $Q$. The goal of this note is to provide a large number of examples of rigid but nonrational and nonreal Lie algebras.

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