Han's conjecture and Hochschild homology for null-square projective algebras

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types with aim providing an inductive step towards proof Firstly show that if algebra $\Lambda$ is triangular respect to a system non necessarily primitive idempotents, and at idempotents belong H$, then in H$. Secondly consider $2\times 2$ matrix algebra, on diagonal, projective bimodules corners, zero corner products. They are not diagonal idempotents. However, analogous result holds, namely both itself