A Characterization of Lie Algebras of Skew-Symmetric Elements

A characterization of Lie algebras of skew-symmetric elements of associative algebras with involution is obtained. It is proved that a Lie algebra L is isomorphic to a Lie algebra of skew-symmetric elements of an associative algebra with involution if and only if L admists and additional (Jordan) trilinear operation {x,y,z} that satisfies the identities {x,y,z} = {z,y,x}, [[x,y],z] = {x,y,z} - {y,x,z}, [{x,y,z},t] = {[x,t],y,z} + {x,[y,t],z} + {x,y,[z,t]}, {{x,y,z},t,v} = {{x,t,v},y,z} - {x,{y,v,t},z} + {x,y,{z,t,v}}, where [x,y] stands for multiplication in L. [PUBLICATION ABSTRACT]