Torsion pairs and Ringel duality for Schur algebras

DOI10.1007/S10468-021-10098-YarXiv2104.05317MaRDI QIDQ6365064

Stacey Law, Karin Erdmann

Publication date: 12 April 2021

Abstract: 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 $k$.

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Representations of associative Artinian rings (16G10) Quantum groups (quantized function algebras) and their representations (20G42) Ring-theoretic aspects of quantum groups (16T20)

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