2013/04/02 by Yuya Mizuno, Mizuno, Yuya · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1304.0667
openalex publication_date 2013/04/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We study support τ-tilting modules over preprojective algebras of Dynkin type. We classify basic support τ-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in bijection with the set of torsion classes, the set of torsion-free classes and other important objects in representation theory. We also study g-matrices of support τ-tilting modules, which show terms of minimal projective presentations of indecomposable direct summands. We give an explicit description of g-matrices and prove that cones given by g-matrices coincide with chambers of the associated root systems.