Etude des ω-PI Algebres Commutatives de Degre 4: II. Algebres Non Barycentriques Invariantes par Gametisation.

In this article we study the algebras satisfying the ω-polynomial identity x2x2 - x4 = δ(x2 - x) with δ ≠ 0 but do not satisfy any monomial identities of degree ≤4. We show that there exist such algebras for all δ ≠ 0 and they have a unique baric function. We give conditions for the existence of idempotents of weight 0 or 1, and we construct the three Peirce decompositions associated to these idempotent elements. [ABSTRACT FROM AUTHOR]