In \cite{a-t}, we defined a $U(\e)$-algebra which is 

a generalization of Freudenthal-Kantor triple system 

defined by I. L. Kantor \cite{k} and K. Yamaguti \cite{y3}. 

In this paper, we call it an FK-ternary algebra. We define 

a representation of the FK-ternary algebra. Moreover we 

define a cohomology space of order 3 of the FK-ternary 

algebra associated with the representation, and give 

an interpretation of this space in relation to extensions 

of the FK-ternary algebra.