Torsion Pairs and Ringel Duality for Schur Algebras

Karin Erdmann; Stacey Law

doi:10.1007/s10468-021-10098-y

Torsion Pairs and Ringel Duality for Schur Algebras

Karin Erdmann
, Stacey Law^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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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 S_q(2,r) in characteristic p > 0 are Morita equivalent as quasi-hereditary algebras to their Ringel duals if they contain 2p^k simple modules for some k.

Original language	English
Pages (from-to)	411–432
Number of pages	22
Journal	Algebras and Representation Theory
Volume	26
Issue number	2
Early online date	23 Sept 2021
DOIs	https://doi.org/10.1007/s10468-021-10098-y
Publication status	Published - Apr 2023

Keywords

Torsion pairs
Ringel duality
Schur algebras

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AU - Law, Stacey

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N2 - 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.

AB - 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.

KW - Torsion pairs

KW - Ringel duality

KW - Schur algebras

U2 - 10.1007/s10468-021-10098-y

DO - 10.1007/s10468-021-10098-y

M3 - Article

SN - 1386-923X

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SP - 411

EP - 432

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 2

ER -

Torsion Pairs and Ringel Duality for Schur Algebras

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Keywords

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