  We calculate the polarization tensor of charged gluons in a Abelian
homogeneous magnetic background field at finite temperature in one loop order
Lorentz background field gauge in full generality. Thereby we first determine
the ten independent tensor structures. For the calculation of the corresponding
form factors we use the Schwinger representation and represent form factors as
double parametric integrals and a sum resulting from the Matsubara formalism
used. The integrands are given explicitly in terms of hyperbolic trigonometric
functions. Like in the case of neutral gluons, the polarization tensor is not
transversal. Out of the tensor structures, seven are transversal and three are
not. The nontransversal part follows explicitly from our calculations.
