The \(p\)-adic group ring of \(\mathrm{SL}_2(p^f)\).

DOI10.1016/j.jalgebra.2014.01.036zbMath1323.20004arXiv1301.7622OpenAlexW1596144936MaRDI QIDQ403127

Florian Eisele

Publication date: 29 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7622

zbMATH Keywords

ordersderived equivalencesBrauer correspondents\(p\)-adic group ringsunique lifting property

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representations of orders, lattices, algebras over commutative rings (16G30) Group rings (16S34) (p)-adic representations of finite groups (20C11) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Representations of finite groups of Lie type (20C33) Orders in separable algebras (16H10) Derived categories and associative algebras (16E35)

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Cites Work

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• \(p\)-adic lifting problems and derived equivalences.
• Broué's conjecture for the nonprincipal block of \(\text{SL}(2,q)\) with full defect.
• Lifting theorems for tilting complexes
• Die Zerlegungsmatrizen der Gruppen \(PSL(2,p^f)\)
• Projective modules for \(SL(2,2^n)\)
• Quiver and relations for \(\text{SL}(2,2^ n)\) in characteristic \(2\)
• The group ring of \(\text{SL}_2(p^f)\) over \(p\)-adic integers for \(p\) odd.
• Degenerations for derived categories
• A NOETHER–DEURING THEOREM FOR DERIVED CATEGORIES
• Quiver and relations forSL(2,pⁿ) in characteristicpwithpodd
• The group ring of SL2(2f) over 2-adic integers
• Derived Equivalences As Derived Functors

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