A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras

2010/06/14 by C. Bowman, S. Martin, Bowman, C. +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1006.2655

openalex publication_date 2010/06/14 · arxiv created 2012/07/16 · arxiv updated 2012/07/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

We show that an adaptation of Landrock's Lemma for symmetric algebras also holds for cellular algebras and BGG algebras. This is a result relating the radical layers of any two projective modules. The reason it holds in our setting is that there is a duality between injective hulls and projective covers. As a corollary we deduce that BGG reciprocity respects Loewy structure.

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