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

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

A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson was established. Some non-trivial with a certain algebra (Witt algebra, $\mathcal{W}(a,-1)$, thin solvable abelian nilpotent radical) were constructed. In particular, we constructed an example the associative parts isomorphic to Laurent polynomials Witt algebra. On other side, it proven that there are no part se...

We introduce the notion of a Lie-like algebra⋄ (superalgebra⋄) for ⋄ ∈ { , , 3−rd }. By bundling a family of algebras, we introduce six new generalizations of Lie algebras which are called Lie-like algebras or Lie-like superalgebras in this paper. The examples of the new generalizations of Lie algebras come from an invariant algebra (or an invariant superalgebra), where the notion of an invaria...

We address the general classification problem of all stable associative product structures in the complex cobordism theory. We show how to reduce this problem to the algebraic one in terms of the Hopf algebra S (the Landweber-Novikov algebra) acting on its dual Hopf algebra S∗ with a distinguished “topologically integral” part Λ that coincids with the coefficient ring of the complex cobordism. ...

Abstract In this paper, we generalize Schur–Weyl duality and Morita Theorem on associative algebras to those H -pseudoalgebras. Meanwhile, get a plenty of -pseudoalgebras over cocommutative Hopf algebra

A necessary and sufficient condition is presented for a graph algebra to satisfy bracketing identity. The associative spectrum of an arbitrary shown be either constant or exponentially growing.