Triangular decompositions: Reedy algebras and quasi-hereditary algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916711777697792 |
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| author | Conde, Teresa Dalezios, Georgios Koenig, Steffen |
| author_facet | Conde, Teresa Dalezios, Georgios Koenig, Steffen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triangular decompositions: Reedy algebras and quasi-hereditary algebras Conde, Teresa Dalezios, Georgios Koenig, Steffen Representation Theory Rings and Algebras 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. |
| title | Triangular decompositions: Reedy algebras and quasi-hereditary algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2411.12912 |