Derived equivalence for cyclic blocks over a \(p\)-adic ring

DOI10.1007/BF02571389zbMath0714.20006OpenAlexW2068440551MaRDI QIDQ750603

Markus Linckelmann

Publication date: 1991

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174270

zbMATH Keywords

blocktilting complexsemidirect productfinite groupbasic algebraBrauer treecyclic defect groupequivalence of derived categories

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) (p)-adic representations of finite groups (20C11) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items

Stable equivalences of Morita type for self-injective algebras and \(p\)-groups, Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups, Une correspondance de modules pour les blocs à groupes de défaut abéliens. (A module correspondence for the blocks of groups with abelian defect), Broué's abelian defect group conjecture and 3-decomposition numbers of the sporadic simple Conway group \(Co_1\)., Coxeter orbits and Brauer trees., Broué's Abelian defect group conjecture holds for the sporadic simple Conway group \(Co_3\)., Lifting theorems for tilting complexes, Broué's Abelian defect group conjecture holds for the Janko simple group \(J_4\)., Pointed Brauer trees, An algorithmic approach to perverse derived equivalences Broué's conjecture for \(\Omega_8^+(2)\), The derived categories of some blocks of symmetric groups and a conjecture of Broué, On Rouquier blocks for finite classical groups at linear primes., Hochschild cohomology and Linckelmann cohomology for blocks of finite groups.

Cites Work

• Pointed groups and construction of characters
• Lifting theorems for tilting complexes
• Modules in the sources of Green's exact sequences for cyclic blocks
• Derived categories and stable equivalence
• Blocks with cyclic defect groups
• Investigations on group characters
• Walking around the Brauer tree
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