Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

DOI10.1007/s00209-019-02301-0zbMath1480.20026arXiv1712.09274OpenAlexW2963449035WikidataQ128096105 ScholiaQ128096105MaRDI QIDQ2288000

Shigeo Koshitani, Caroline Lassueur

Publication date: 16 January 2020

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

Full work available at URL: https://arxiv.org/abs/1712.09274

zbMATH Keywords

Morita equivalencesplendid Morita equivalencedihedral 2-groupstable equivalence of Morita typeBrauer indecomposabilityScott modulegeneralised decomposition numbersPuig's finiteness conjecture

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Module categories in associative algebras (16D90) Modular representations and characters (20C20) Representations of finite groups of Lie type (20C33)

Related Items (8)

The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$ ⋮ Splendid Morita equivalences for principal blocks with generalised quaternion defect groups ⋮ Relative stable equivalences of Morita type for the principal blocks of finite groups and relative Brauer indecomposability ⋮ The group of splendid Morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups ⋮ REAL BLOCKS WITH DIHEDRAL DEFECT GROUPS REVISITED ⋮ The Brauer indecomposability of Scott modules with wreathed 2-group vertices ⋮ Splendid Morita equivalences for principal blocks with semidihedral defect groups ⋮ Brauer indecomposability of Scott modules with semidihedral vertex

Cites Work

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• Brauer indecomposability of Scott modules
• Broué's Abelian defect group conjecture holds for the sporadic simple Conway group \(Co_3\).
• On Brauer indecomposability of Scott modules of Park-type groups.
• The structure of blocks with a Klein four defect group.
• On saturated fusion systems and Brauer indecomposability of Scott modules.
• Real subpairs and Frobenius-Schur indicators of characters in 2-blocks.
• Group rings of finite groups over p-adic integers
• Almost-split sequences and group rings
• Characters and local structure in G-algebras
• A remark on blocks with dihedral defect groups in solvable groups
• Blocks of tame representation type and related algebras
• Isomorphic blocks
• Remarks on isomorphic blocks
• On the local structure of Morita and Rickard equivalences between Brauer blocks
• A derived equivalence for blocks with dihedral defect groups
• Blocks and source algebras for the double covers of the symmetric and alternating groups
• Scopes reduction and Morita equivalence classes of blocks in finite classical groups
• Broué's conjecture holds for principal 3-blocks with elementary Abelian defect group of order 9
• Scopes reduction and Morita equivalence classes of blocks in finite classical groups. II.
• The isomorphism problem for cyclic blocks and their source algebras
• Stable equivalences of Morita type for self-injective algebras and \(p\)-groups
• On finite groups with dihedral Sylow 2-subgroups
• The characterization of finite groups with dihedral Sylow 2-subgroups. I, II
• Some applications of the theory of blocks of characters of finite groups. I
• Some applications of the theory of blocks of characters of finite groups. III
• Fusion systems on small 𝑝-groups
• ON THE BRAUER INDECOMPOSABILITY OF SCOTT MODULES
• Relative projective covers and almost split sequences
• On Scott Modules and p-Permutation Modules: An Approach through the Brauer Morphism
• Principal blocks of groups with dihedral sylow 2-subgroups
• The homotopy theory of fusion systems
• The Block Theory of Finite Group Algebras
• Equivalences for blocks of the Weyl groups
• Scopes reduction for blocks of finite alternating groups
• Splendid Equivalences: Derived Categories and Permutation Modules
• The Representations of GL(3,q), GL(4,q), PGL(3,q), and PGL(4,q)
• The Auslander-Reiten quiver of a finite group
• Source algebra equivalences for blocks of finite general linear groups over a fixed field
• On splendid derived and stable equivalences between blocks and finite groups

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