Gluing support $τ$-tilting modules via symmetric ladders of height 2

Yingying Zhang

Published 2021-05-20Version 1

Recent result by Adachi-Iyama-Reiten has shown a bijective correspondence between support $\tau$-tilting modules and functorially finite torsion classes. On the other hand, the techniques of gluing torsion classes along a recollement were investigated by Liu-Vit\'oria-Yang and Ma-Huang. In this article, we show that gluing torsion classes can be restricted to functorially finiteness condition in the symmetric ladders of height 2. Then using the above correspondence with support $\tau$-tilting modules, we present explicit constructions of gluing of support $\tau$-tilting modules via symmetric ladders of height 2. Finally, we apply the results to triangular matrix algebras to give a more detailed version of the known Jasso's reduction and study maximal green sequences.