Torsion Pairs and Ringel Duality for Schur Algebras
| Autor: | Stacey Law, Karin Erdmann |
|---|---|
| Přispěvatelé: | Law, S [0000-0001-7936-0938], Apollo - University of Cambridge Repository |
| Rok vydání: | 2023 |
| Předmět: |
Pure mathematics
Endomorphism Ringel duality General Mathematics Mathematics::Rings and Algebras Duality (mathematics) Schur algebra Torsion pairs Schur algebras Mathematics::K-Theory and Homology ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Torsion (algebra) Dual polyhedron Representation Theory (math.RT) Algebraically closed field Mathematics::Representation Theory Simple module Quantum Mathematics - Representation Theory Mathematics |
| DOI: | 10.17863/cam.95576 |
| Popis: | Acknowledgements: We are grateful to the anonymous reviewer for their helpful corrections that have improved the clarity of our exposition. The second author was supported by a London Mathematical Society Early Career Fellowship at the University of Oxford. Let $A$ be a finite-dimensional algebra over a field of characteristic $p>0$. We use a functorial approach involving torsion pairs to construct embeddings of endomorphism algebras of basic projective $A$--modules $P$ into those of the torsion submodules of $P$. As an application, we show that blocks of both the classical and quantum Schur algebras $S(2,r)$ and $S_q(2,r)$ are Morita equivalent as quasi-hereditary algebras to their Ringel duals if they contain $2p^k$ simple modules for some $k$. |
| Databáze: | OpenAIRE |
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