Duality in G-algebras

DOI10.1007/BF01161746zbMath0667.20008OpenAlexW1555593722MaRDI QIDQ1117315

Jacques Thévenaz

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf01161746

zbMATH Keywords

defect groupsblockalmost split sequencesfinite groupsymmetric algebrasymmetric bilinear formprojective idealvirtually irreducible latticesRG-latticecomplete discrete valuation ringsplitting trace latticesalmost projective idealsymmetric G-algebraunimodular symmetric G-algebra

Mathematics Subject Classification ID

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) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items (13)

Stable equivalences of Morita type for self-injective algebras and \(p\)-groups ⋮ A characterisation of nilpotent blocks ⋮ \(G\)-algebras, Clifford theory, and the Green correspondence ⋮ A note on vertices of indecomposable tensor products ⋮ On Tate duality and a projective scalar property for symmetric algebras ⋮ Knörr lattices, their characters, and some subsets of \(\mathbb F^d_p\). ⋮ Relative projectivity of trace zero endomorphisms ⋮ Restriction between cohomology algebras of blocks of finite groups. ⋮ On Auslander-Reiten components and height zero lattices for integral group rings. ⋮ Anchors of irreducible characters ⋮ On Auslander-Reiten components and trivial modules for integral group rings of \(p\)-groups ⋮ The parametrization of interior algebras ⋮ On Thévenaz' parametrization of interior \(G\)-algebras

Cites Work

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• Subgroups and almost split sequences of a finite group
• Functors on categories of finite group representations
• Almost-split sequences and group rings
• Bilinear forms on G-algebras
• Quelques remarques sur un thème de Knörr. (Some remarks on a theme of Knörr)
• Nilpotent blocks and their source algebras
• Pointed groups and construction of modules
• Pointed groups and construction of characters
• Remarks on blocks and subgroups
• Algebras and Dihedral Defect Groups
• Some remarks on G-functors and the Brauer morphism.
• Virtually Irreducible Lattices
• An Exponential Property of Lattices Over Group Rings
• The construction of almost split sequences for integral group rings and orders
• Radical, hauteurs, p-sections et blocs

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