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On the classification of nil algebras of nil index 3. (Sur la classification des nil algèbres commutatives de nil indice 3.) (French) Zbl 1094.17001
As noted by S. Walcher, any commutative (not necessarily associative) nilagebras \(N\) of index \(3\) is a Jordan algebra, and therefore nilpotent. In the present paper, the authors obtain some results on the structure of these algebras. As an application of their results, they present a new way of classifying these nilalgebras \(N\) when \(\dim N\leq 6\).

MSC:
17A30 Nonassociative algebras satisfying other identities
17C50 Jordan structures associated with other structures
17D92 Genetic algebras
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