Journal of Generalized Lie Theory and Applications

The aim of this paper is to investigate the cohomologies for ternary algebras of associative type.We study in particular the cases of partially associative ternary algebras and weak totally associative ternary algebras. Also, we consider the Takhtajan's construction, which was used to construct a cohomology of ternary Nambu-Lie algebras using Chevalley-Eilenberg cohomology of Lie algebras, and discuss it in the case of ternary algebras of associative type. One of the main results of this paper states that a usual deformation cohomology does not exist for partially associative ternary algebras which implies that their operad is not a Koszul operad.

The purpose of the present paper is to consider and study a special form of Rund's h-curvature tensor Ki ljk and Berwald's curvature tensor Hi ljk in an R3-like C-reducible Finsler space. In this paper, we modify the Rund's h-curvature tensor Ki ljk to special form by using some special Finsler spaces like C-reducible, R3-like Finsler spaces.

It is known that the Betti numbers of the Heisenberg Lie algebras are unimodal over elds of characteristic two. This note observes that they are log-concave. An example is given of a nilpotent Lie algebra in characteristic two for which the Betti numbers are unimodal but not log-concave.

We construct Lie superalgebras osp(2n + 1 j 4n + 2) and osp(2n j 4n) starting with certain classes of anti-structurable algebras via the standard embedding Lie superalgebra construction corresponding to (; )-Freudenthal Kantor triple systems.