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arXiv · 1812.04871

Maximal $τ_d$-rigid pairs

Karin M. Jacobsen·Peter Jorgensen
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Abstract

Let $\mathscr T$ be a $2$-Calabi--Yau triangulated category, $T$ a cluster tilting object with endomorphism algebra $Γ$. Consider the functor $\mathscr T( T,- ) : \mathscr T \rightarrow \mod Γ$. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support $τ$-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of $( d+2 )$-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal $τ_d$-rigid pairs.

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BibTeXRIS

Karin M. Jacobsen, Peter Jorgensen. 2019-10-25. Maximal $τ_d$-rigid pairs. https://doi.org/10.1016/j.jalgebra.2019.10.046

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