On the structure of Calabi-Yau categories with a cluster tilting subcategory

TL;DR

This paper demonstrates that algebraic d-Calabi-Yau triangulated categories with a d-cluster tilting subcategory can be realized as stable categories of DG categories with specific Calabi-Yau and t-structure properties, advancing understanding of their structure.

Contribution

It establishes a structural characterization of algebraic d-Calabi-Yau categories with cluster tilting subcategories as stable categories of certain DG categories with Calabi-Yau and t-structure features.

Findings

Categories are stable categories of DG categories with Calabi-Yau properties

Existence of a non-degenerate t-structure with enough projectives in the heart

Extension of Calabi-Yau and cluster tilting theory to higher dimensions

Abstract

We prove that for $d \geq 2$, an algebraic $d$-Calabi-Yau triangulated category endowed with a $d$-cluster tilting subcategory is the stable category of a DG category which is perfectly $(d+1)$-Calabi-Yau and carries a non degenerate $t$-structure whose heart has enough projectives.