Stratifying systems through $τ$-tilting theory

Abstract

In this paper we study the stratifying systems, introduced by K. Erdmann and C. Saenz in [17], by using the τ -tilting theory introduced by T. Adachi, O. Iyama and I. Reiten in [1]. We give a constructive proof that every non-zero τ -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 τ -exceptional sequence as defined by A. B. Buan and R. Marsh in [5].