Tilting theory of preprojective algebras and c-sortable elements

2014/05/16 by Yuta Kimura, Kimura, Yuta
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1405.4087

openalex publication_date 2014/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite acyclic quiver Q and the corresponding preprojective algebra Π, we study the factor algebra Π_w associated with a element w in the Coxeter group introduced by Buan-Iyama-Reiten-Scott. The algebra Π_w has a natural ℤ-grading, and we prove that \underlineSub^ℤΠ_w has a tilting object M. Moreover, we show that the endomorphism algebra of M is isomorphic to the stable Auslander algebra of a certain torsion free class of mod kQ.

Related

• Tilting and cluster tilting for preprojective algebras and Coxeter groups
• APR tilting modules and graded quivers with potential
• Another characterization of tilted algebras
• A pre-projective part of tilting quivers of certain path algebras
• Some applications of τ-tilting theory