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Train algebras of degree 2 and exponent 3

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  • In this paper we investigate the structure of weighted algebras satisfying the equation $(x^3)^2 = \omega(x)^3x^3$, a class of algebras properly containing the class of Bernstein algebras. We give the classification of these algebras in dimension three. Some results about the structure of algebras satisfying the more general equation $(x^n)^2 = \omega(x)^nx^n$, for $n\geq 2$, are also obtained.
    Mathematics Subject Classification: Primary: 17D92; Secondary: 17A30.

    Citation:

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  • [1]

    A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc., 69 (1950), 503-527.

    [2]

    I. Basso, R. Costa, J. Carlos Gutiérrez and H. Guzzo Jr., Cubic algebras of exponent $2$: Basic properties, Int. J. Math. Game Theory and Algebra, 9 (1999), 245-258.

    [3]

    J. Bayara, A. Conseibo and M. Ouattara et F. Zitan, Power-associative algebras that are train algebras, J. Algebra, 324 (2010), 1159-1176.doi: 10.1016/j.jalgebra.2010.06.012.

    [4]

    H. Guzzo Jr. and P. Vicente, Train algebras of rank $n$ which are Bernstein or power-associative algebras, Nova J. Math. Game Theory Algebra, 6 (1997), 103-112.

    [5]

    H. Guzzo Jr., The Peirce decomposition for commutative train algebras, Comm. Algebra, 22 (1994), 5745-5757.doi: 10.1080/00927879408825160.

    [6]

    J. Lopez Sanchez and E. Rodriguez S. Maria, On train algebras of rank $4$, Comm. Algebra, 24 (1996), 4439-4445.doi: 10.1080/00927879608825825.

    [7]

    A. Micali and M. Ouattara, Structure des algèbres de Bernstein, Linear Algebra Appl., 218 (1995), 77-88.doi: 10.1016/0024-3795(93)00159-W.

    [8]

    M. Ouattara, Sur les T-algèbres de Jordan, Linear Algebra Appl., 144 (1991), 11-21.doi: 10.1016/0024-3795(91)90056-3.

    [9]

    M. Ouattara, Sur une classe d'algèbres à puissances associatives, Linear Algebra Appl., 235 (1996), 47-62.doi: 10.1016/0024-3795(94)00113-8.

    [10]

    R. D. Schafer, "An Introduction to Nonassociative Algebras," Academic Press, New York, 1966.

    [11]

    S. Walcher, On Bernstein algebras which are train algebras, Proc. Edinb. Math. Soc. (2), 35 (1992), 159-166.doi: 10.1017/S0013091500005411.

    [12]

    S. Walcher, Algebras which satisfy a train equation for the first three plenary powers, Arch. Math. (Basel), 56 (1991), 547-551.

    [13]

    A. Wörz-Busekros, "Algebras in Genetics," Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980.

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