There exist two types of non-associative
algebras whose associator satisfies a symmetric relation associated with a
1-dimensional invariant vector space with respect to the natural action of the
symmetric group Σ3. The first one corresponds to the Lie-admissible algebrasand this class has been studied in a previous paper of Remm and Goze. Here we
are interested by the second one corresponding to the third power associative
algebras.
Recently, we have classified for
binary algebras, Cf., relations of no associativity which are invariant with
respect to an action of the symmetric group on three elements Σ3 on the
associator. In particular we have investigated two classes of no associativealgebras.
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