Generalization of n-ary Nambu algebras and beyond

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

Nambu-Poisson manifolds and associated n-ary Lie algebroids

We introduce an n-ary Lie algebroid canonically associated to a NambuPoisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize such operators. Some physical examples are presented.

Hopf Structure in Nambu-Lie n-Algebras

We give a definition and study Hopf structures in ternary ( and n-ary) NambuLie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra and Hopf 3algebra are introduced. Some examples of Hopf structures are analyzed. Mathematics Subject Classification (1991) 70H99, 58F07 1 [email protected] 2 [email protected] In 1973 Yoishira Nambu [1] proposed a generalization of classical Hamiltonian mecha...

Varieties of Anticommutative n-ary Algebras

A fundamental problem in the theory of n-ary algebras is to determine the correct generalization of the Jacobi identity. This paper describes some computational results on this problem using representations of the symmetric group. It is well known that over a field of characteristic 0 any variety of n-ary algebras can be defined by multilinear identities. In the anticommutative case, it is show...

n-ary associative algebras, cohomology, free algebras and coalgebras

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...