Sur les T-algèbres de Jordan

Power-associative algebras that are train algebras

“…We emphasize that such algebras are no longer Jordan algebras [21,Exemple 2.2], so that 3 is the best rank in Corollary 4.4. At present, we give a criterion for some power-associative train algebras of rank 5 to be Jordan.…”

“…In [26], Schafer discovered the presence of some Jordan algebras among train algebras, through the gametic and zygotic algebras for simple Mendelian inheritance (see also [12]). Motivated by these results, Ouattara presented subsequently a study on Jordan train algebras in a more general context [21]. Later, Guzzo and Vicente [10] found the coefficients of the train equation of a powerassociative train algebra.…”

“…By Corollary 2.5, there are exactly r − 1 possible presentations (or train equations) for powerassociative train algebras of rank r. We note in passing that, contrarily to the case when rank A 3 (see[21, Théorème 2.1] or [10, Proposition 2.2]), a train algebra of presentation (s, t) need not be power-associative. In fact, for each r 4, it has been exhibited in [10, Example 1] a train algebra of presentation (r − 1, 1) which is not power-associative.…”

Baric, bernstein and jordan algebras

“…r : % as the following example shows. It 1s known (see [12]) that if A is a train algcbra of rank 3 the11 the t l r r t~ statements. namely.…”

Álgebras train

“…Em [28], Schafer descobriu a presença de algumasálgebras de Jordan entre asálgebras train. Motivados por estes resultados, Ouattara subsequentemente apresentou um estudo sobre asálgebras train de Jordan em um contexto mais geral [23].…”