Triangular decompositions: Reedy algebras and quasi-hereditary algebras
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.
Fields of Study & Subjects
Advanced Topics in Algebra
Rings
Modules
and Algebras
Advanced Algebra and Logic
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4631–4647
- Publication date
- 27 May 2026
- Language
- EN