Abstract
For an abelian group G we consider braiding in a category of G-graded modules
M
kG
given by a bicharacter \chi on G. For
(G,χ)
-bialgebra A in
M
kG
an analog of Lie bracket is defined. This bracket is determined by a linear map $E\in\End(A)$ and n-ary operations
Ω
n
E
on A. Our result states that if
E(1)=0,
E
2
=0
and
Ω
3
E
=0
then a braided Jacobi identity holds and the linear map E is a braided derivation of a braided Lie algebra.