Amar Makhlouf

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The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type enclosing n-ary Nambu algebras, n-ary Nambu-Lie algebras, n-ary Lie algebras, and n-ary algebras of associative type enclosing n-ary totally associative and n-ary partially associative algebras. Also, we provide a way to construct examples starting(More)
We apply the averaging theory of first and second order to a class of polynomial differential systems of the form ẋ = y − f1(x)y, ẏ = −x − g2(x)− f2(x, y)y, where f1(x) = εf11(x) + εf12(x), f2(x, y) = εf21(x, y) + εf22(x, y) and g2(x) = εg21(x)+ εg22(x) where f1i , f2i and g2i have degree l, n and m respectively for each i = 1, 2, and ε is a small(More)
A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α, β : A → A such that α(a)(bc) = (ab)β(c), for all a, b, c ∈ A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and(More)
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