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

TL;DR

This paper introduces explicit methods for gluing support τ-tilting modules using symmetric ladders of height two, with applications to triangular matrix algebras and maximal green sequences.

Contribution

It provides new explicit constructions for gluing support τ-tilting modules via symmetric ladders of height two, extending existing theories.

Findings

Explicit construction methods for gluing support τ-tilting modules.

Application to triangular matrix algebras and detailed Jasso's reduction.

Analysis of maximal green sequences in the context of the new constructions.

Abstract

Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. We present explicit constructions of gluing of support $\tau$-tilting modules via symmetric ladders of height two. Moreover, we apply the result to triangular matrix algebras to give a more detailed version of the known Jasso's reduction and study maximal green sequences.