Cohomologie des alg\`{e}bres de Kr\"{o}necker g\'{e}n\'{e}rales

The computation of the Hochschild cohomology $H{H}^{\ast }(T)=H^{\ast }(T,T)$ of a triangular algebra T=\pmatrix{A&M\cr 0&B\cr} was performed in {\bf[BG2]}, by the means of a certain triangular complex. We use this result here to show how $H{H}^{\ast }(T)$ splits in little pieces whenever the bimodule $M$ is decomposable. As an example, we express the Hilbert-Poincar'{e} serie $\sum_{i=0}^\infty dim_K HH^i(T_m)t^i$ofthe\mathrm{"}general\mathrm{"}Kr\ddot{o}neckeralgebra$T_m=\pmatrix{A&M^m\cr 0&B\cr}$asafunctionof$m\geq 1$andthoseof$T$(herethegroundring$K$isafieldand$dim_K T<+\infty$). The Lie algebra structure of $H{H}^1(T)$ is also considered.