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GENERALIZED ALMOST JORDAN NILALGEBRAS OF NILINDEX FOUR AND DIMENSION AT MOST FIVE
Keywords:
Generalized almost jordan algebra, nilalgebra, nilindex, nilpotence, power-associativity.DOI:
https://doi.org/10.17654/0972555526008Abstract
We study the generalized almost-Jordan nilalgebras of nilindex four that are not power associative. We first give some interesting equalities in these algebras. These equalities enable to find the possible multiplication tables relative to the dimension. We have one table in dimension three and two in dimension four. In dimension five, we show that the dimension of the square of an algebra satisfying these conditions is either 2 or 3, which shows four possible multiplication tables in dimension five.
Received: July 29, 2025
Revised: August 25, 2025
Accepted: September 3, 2025
References
[1] L. Carini, I. R. Hentzel and G. M. Piacentini Cattaneo, Degree four identities not implied by commutativity, Comm. Algebra 16(2) (1988), 339-356.
[2] A. Elduque and A. Labra, On the classification of commutative right-nilalgebras of dimension at most four, Comm. Algebra 35(2) (2007), 577-588.
doi:10.1080/00927870601074780.
[3] Juan C. Gutiérrez Fernandez, Commutative finite-dimensional algebras satisfying are nilpotent, Comm. Algebra 37(10) (2009), 3760-3776.
doi:10.1080/00927870802502944.
[4] I. R. Hentzel and A. Labra, Generalized Jordan algebras, Linear Algebra Appl. 422 (2007), 326-330.
[5] J. M. Osborn, Varieties of algebras, Adv. Math. 8 (1972), 163-369.
doi:10.1016/0001-8708(72)90003-5.
[6] R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966.
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