K\"ulshammer ideals of graded categories and Hochschild cohomology

We generalize the notion of K\"ulshammer ideals to the setting of a graded category. This allows us to define and study some properties of K\"ulshammer type ideals in the graded center of a triangulated category and in the Hochschild cohomology of an algebra, providing new derived invariants. Further properties of K\"ulshammer ideals are studied in the case where the category is $d$-Calabi-Yau.