Topics on n-ary algebras

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

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...

On the N-ary Algebras and Their Universal Covers

For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. We discuss the properties of the construction and two simple examples. 1991 Mathematics Subject Classification: 17A42, 16Y99, 17A40

On the n-ary algebras, semigroups and their universal

For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups. AMS Classification: 17A42, 16N34, 20N15