  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 deformation cohomology does
not exist for partially associative ternary algebras which implies that their
operad is not a Koszul operad.
