A contragredient Lie algebra of dimension 29 over a field of characteristic 3

Two contragredient Lie algebras over a field of characteristic 3 are studied. The Lie algebras are shown to be isomorphic to the simple 29-dimensional Lie algebra constructed earlier by Brown. An example is presented of a simple finite-dimensional contragredient Lie algebra absent in the list of B. Yu. VeTsfeller and V. G. Kats.