# Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

Published in Comm. Algebra, January 2021. Links: journal, arXiv:2002.09205

Citation: H. Enomoto, Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras, Comm. Algebra 49 (2021), no. 5, 2156--2189.

## Comment

As a generalization of the study of torsion-free classes over type A quiver in my JHP paper, we consider preprojective algebras and path algebras of Dynkin type and classify simples in their torsion-free classes $\mathcal{F}_w$ (Buan-Iyama-Reiten-Scott’s category $\mathcal{C}_w$) by using its relation with the root system. I also give a method to find simples in a torsion-free class $\mathcal{F}$ by using maximal green sequence of $\mathcal{F}$ (or a path in the Hasse quiver from $\mathcal{F}$ to $0$) via their brick labeling by [DIRRT].