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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)
Let B ⊆ A be an H-Galois extension. If M is a Hopf bimodule then HH * (A, M), the Hochschild homology of A with coefficients in M , is a right comodule over the coalgebra C H = H/[H, H]. Given an injective left C H-comodule V , our aim is to investigate the relationship between HH * (A, M) CH V and HH * (B, M CH V). The roots of this problem can be found in… (More)
In this paper some fixed point principle is applied to prove, in a separable Banach space, the existence of solutions for delayed second order differential inclusions with three-point boundary conditions of the form ¨ u(t) ∈ F (t, u(t), u(h(t)), ˙ u(t)) + H(t, u(t), u(h(t)), ˙ u(t)) a.e. t ∈ [0, 1], where F is a convex valued multifunction upper semi… (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)
Applying the averaging theory of first and second order to a class of generalized polynomial Liénard differential equations, we improve the known lower bounds for the maximum number of limit cycles that this class can exhibit.