  We introduce the generalized Heisenberg algebra appropriate for realizations
of the $\mathfrak{gl}(n)$ algebra. Linear realizations of the
$\mathfrak{gl}(n)$ algebra are presented and the corresponding star product,
coproduct of momenta and twist are constructed. The dual realization and dual
$\mathfrak{gl}(n)$ algebra are considered. Finally, we present a general
realization of the $\mathfrak{gl}(n)$ algebra, the corresponding coproduct of
momenta and two classes of twists. These results can be applied to physical
theories on noncommutative spaces of the $\mathfrak{gl}(n)$ type.
