2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94873The computation of the Hochschild cohomology $HH^*(T)=H^*(T,T)$ 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 $HH^*(T)$ splits in little pieces whenever the bimodule $M$ is decomposable. As an example, we express the Hilbert-Poincaré serie $\sum\_{i=0}^\infty dim\_K HH^i(T\_m)t^i$ of the "general" Krönecker algebra $T\_m=\pmatrix{A&M^m\cr 0&B\cr}$ as a function of $m\geq 1$ and those of $T$ (here the ground ring $K$ is a field and $dim\_K T<+\infty$). The Lie algebra structure of $HH^1(T)$ is also considered.K-Theory and Homology13D40, 16G60, 16E05, 16E30, 16E40, 16E45, 20G05, 20F40, 13J05text