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

Gao, Nan; Koenig, Steffen; Psaroudakis, Chrysostomos

doi:10.1090/proc/14620

Recollements of abelian categories and ideals in heredity chains—a recursive approach to quasi-hereditary algebras
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by Nan Gao, Steffen Koenig and Chrysostomos Psaroudakis PDF

Proc. Amer. Math. Soc. 147 (2019), 4625-4637 Request permission

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 occurring 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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