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This paper investigates bicovariant differential calculus on noncommutativespaces of the Lie algebra type. For a given Lie algebra $g_0$ we construct aLie superalgebra $g=g_0\oplus g_1$ containing noncommutative coordinates andone--forms. We show that $g$ can be extended by a set of generators $T_{AB}$whose action on the enveloping algebra $U(g)$ gives the commutation relationsbetween monomials in $U(g_0)$ and one--forms. Realizations of noncommutativecoordinates, one--forms and the generators $T_{AB}$ as formal power series in asemicompleted Weyl superalgebra are found. In the special case $dim(g_0)=dim(g_1)$ we also find a realization of the exterior derivative on $U(g_0)$.The realizations of these geometric objects yield a bicovariant differentialcalculus on $U(g_0)$ as a deformation of the standard calculus on the Euclideanspace.

Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces