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Gametization of weighted algebras. (Gamétisation d’algèbres pondérées.) (French) Zbl 1134.17312
Summary: The authors introduce the notion of gametization of a baric (weighted) algebra as a simple tool that allows to study structures that fulfil the \(\omega\)-polynomial identities. For train-identities of arbitrary order they establish the existence of invariant identities by gametization and their form is made precise. Classification results are given here for algebras of order \(\leq 4\).

MSC:
17D92 Genetic algebras
17A30 Nonassociative algebras satisfying other identities
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