Radically filtered quasi-hereditary algebras and rigidity of tilting modules

2015/01/28 by Amit Hazi, Hazi, Amit
Mathematics · #16D70 (Primary) #16D90 #20G40 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D70 #msc:16D90 #msc:20G40

paper · pdf · doi:10.48550/arxiv.1501.07066

24 pages, 1 figure

openalex publication_date 2015/01/28 · arxiv created 2015/06/08 · arxiv updated 2015/06/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let A be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend more than one layer in the radical series or the socle series. We apply this theorem to give new results about the radical series of some tilting modules for SL₄(K), where K is a field of positive characteristic.

Related

• Tilting theoretic approach to quasi-hereditary structures
• A new characterization of hereditary algebras
• Characteristic tilting modules and Ringel duality in the Noetherian world
• τ-rigid modules for algebras with radical square zero
• Tilting-completion for gentle algebras