Beijing Institute of Mathematical Sciences and Applications

Yu Qiu

Lihao Ni

Saturday, April 25, 2026 2:00 PM - 3:00 PM

A3-4-101

Zoom 293 812 9202 (BIMSA)

We can establish a precise connection between $d$-cluster tilting objects in the $d$-cluster category $\mathcal{C}_d(\mathcal{H})$ and $\tau_{[d]}$-tilting pairs in the $d$-extended module category $d\text{-}\mathcal{H}$. The correspondence is mediated by $(d+1)$-term silting complexes in the homotopy category $\mathcal{K}$. Moreover, we relate silting mutations to d-cluster tilting mutations, showing that the $d$-cluster tilting quiver can be obtained from the $(d+1)$-term silting quiver by adding specific arrows. These results unify the combinatorial mutation structures of higher cluster categories with silting theory and $\tau_{[d]}$-tilting theory in extended module categories.