Recollements of abelian categories and ideals in heredity chains - a recursive approach to quasi-hereditary algebras

2018/04/24 by Nan Gao, Gao, Nan, Steffen Koenig +3
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1804.08848

openalex publication_date 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity chains, which in turn characterises quasi-hereditary algebras recursively. Further applications are given to hereditary algebras and to Morita context rings.

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