Sur la cohomologie des algèbres de type An

We are interested here in the Hochschild cohomology of tensor triangular algebras $\text{T}$. We describe in particular a spectral sequence, whose terms are parametrized by the lengths of the trajectories of the quiver associated with $\text{T}$, and which converges to $\text{HH}{}^1\text{(}\text{T}\text{)}$, the Hochschild cohomology of $\text{T}$. Differentials at the first level are sums of cup products. To cite this article: S. Dourlens, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 527–532.