# K\"ulshammer ideals of graded categories and Hochschild cohomology

## TL;DR

This paper extends K"ulshammer ideals to graded categories, exploring their properties in the graded center and Hochschild cohomology, and introduces new derived invariants, especially in the context of $d$-Calabi-Yau categories.

## Contribution

It generalizes K"ulshammer ideals to graded categories and studies their properties, providing new tools for invariants in derived and Hochschild cohomology.

## Key findings

- K"ulshammer ideals are extended to graded categories.
- Properties of these ideals are analyzed in the graded center and Hochschild cohomology.
- Special properties are identified for $d$-Calabi-Yau categories.

## Abstract

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.