Abstract
In this paper, we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on sl(2,C) and iso(1, 3) the Poincaré algebra in four dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.
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