Stratifying systems through $τ$-tilting theory

Octavio Mendoza, Hipolito Treffinger

Published 2019-04-26Version 1

In this paper we study the stratifying systems, introduced by K. Erdmann and C. Saenz in \cite{Erdmann2003}, by using the $\tau$-tilting theory introduced by T. Adachi, O. Iyama and I. Reiten in \cite{AIR}. We give a constructive proof that every non-zero $\tau$-rigid module induces at least one stratifying system for any finite dimensional algebra $A$. Later, we show that each stratifying system found this way is a $\tau$-exceptional sequence as defined by A. B. Buan and R. Marsh in \cite{BM}.