Abstract:
It is proved that the property of being a semisimple algebra is
preserved under projections (lattice isomorphisms) for locally
finite-dimensional Lie algebras over a perfect field of
characteristic not equal to 2 and 3, except for the projection of a
three-dimensional simple nonsplit algebra. Over fields with the
same restrictions, we give a lattice characterization of a
three-dimensional simple split Lie algebra and a direct product of a
one-dimensional algebra and a three-dimensional simple nonsplit one.
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