Abstract
Let A be a finite-dimensional algebra over an algebraically closed field. 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 Sq(2,r) in characteristic p > 0 are Morita equivalent as quasi-hereditary algebras to their Ringel duals if they contain 2pk simple modules for some k.
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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.
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Presented by: Andrew Mathas
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Erdmann, K., Law, S. Torsion Pairs and Ringel Duality for Schur Algebras. Algebr Represent Theor 26, 411–432 (2023). https://doi.org/10.1007/s10468-021-10098-y
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DOI: https://doi.org/10.1007/s10468-021-10098-y