Work

Triangular decompositions: Reedy algebras and quasi-hereditary algebras

Year: 2026

Type: article

Abstract: Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-hereditary algebras admitting a triangular (or Poincaré–Birkhoff–Witt type) decomposition into the tensor product of two oppositely directed subalgebras over a common semisimple subalgebra. This exhibits homological and representation-theoretic structure of the ingredients of the Reedy decomposition and it allows to give a characterisation of Reedy algebras in terms of idempotent ideals occurring in heredity chains, providing an analogue for Reedy algebras of a result of Dlab and Ringel on quasi-hereditary algebras.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17769

Authors: Teresa Conde, Georgios Dalezios, Steffen Koenig

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft

Awards: G6601682123, TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie

OpenAlex ID: W4404648573

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