A construction for affine quasi-hereditary algebras

Key Points

Affine quasi-hereditary algebras can be defined by certain idempotents and quotient structures, which is a critical finding.
The core evidence shows that if an algebra H meets specific conditions, it retains affine quasi-hereditary nature across its substructures.
Using the generalization, the study provides a new proof regarding triangular matrix algebras linked to affine quasi-hereditary algebras.
These findings highlight the deeper structural connections within algebra theory, paving the way for future research on related algebraic systems.

Abstract

We prove that Dlab and Ringel's result in Citation5, Thm. 1 can be generalized to affine quasi-hereditary algebras. To be precise, under particular conditions, for an algebra H and an idempotent e∈H, H is affine quasi-hereditary if and only if eHe and H/HeH are affine quasi-hereditary. As an application, we give a new proof that triangular matrix algebras over affine quasi-hereditary algebras are affine quasi-hereditary.

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Guiyu Yang (Fri,) studied this question.

synapsesocial.com/papers/68a368780a429f797332d778 https://doi.org/https://doi.org/10.1080/00927872.2025.2537281

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