Lifting theorems for tilting complexes

DOI10.1016/0021-8693(91)90313-WzbMath0799.16014OpenAlexW2079455113MaRDI QIDQ1178924

Jeremy Rickard

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1016/0021-8693(91)90313-w

zbMATH Keywords

derived categoriesgroup algebratilting complexesmodule categorieslifting theorems\({\mathcal O}G\)-lattice

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Module categories in associative algebras (16D90) Group rings (16S34) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items (14)

Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring. ⋮ Universal deformation rings and self-injective Nakayama algebras ⋮ The \(p\)-adic group ring of \(\mathrm{SL}_2(p^f)\). ⋮ Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth ⋮ Coxeter orbits and Brauer trees. ⋮ Bijections of silting complexes and derived Picard groups ⋮ Tilting hereditary orders ⋮ \(p\)-adic lifting problems and derived equivalences. ⋮ Pointed Brauer trees ⋮ Homogeneous Deformations of Brauer Tree Algebras ⋮ Derived equivalence for cyclic blocks over a \(p\)-adic ring ⋮ Two-sided tilting complexes for Gorenstein orders ⋮ Co-existence of Krull filtrations ⋮ Tilting and trivial extensions

Cites Work

• Derived equivalence for cyclic blocks over a \(p\)-adic ring
• Derived categories and stable equivalence
• Morita Theory for Derived Categories
• Deformations of Finite Dimensional Algebras and Their Idempotents
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• Derived Equivalences As Derived Functors
• A lifting theorem for modular representations
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