The graded centre of a triangulated category is the \(\mathbb Z\)-graded ring whose degree \(n\) component is formed by those natural transformations of the identity to the degree \(n\) suspension which commute up to sign \((-1)^n\) with the suspension. The graded centre was used recently to study a new connection between the derived category and the Hochschild cohomology of a ring. Linckelmann computed the case of a derived category of a Brauer tree algebra. Explicit examples were rarely available.
The paper under review computes explicitly the case of the bounded derived category of a Dedekind domain, the case of tame hereditary algebras, the case of the weighted projective line, and the case of the stable and the bounded derived category of the truncated polynomial ring \(k[X]/X^n\). On the way the authors show various interesting reduction techniques for this problem.