Induction formulae for Mackey functors with applications to representations of the twisted quantum double of a finite group

DOI10.1016/j.jalgebra.2014.03.017zbMath1298.19002OpenAlexW2000058780MaRDI QIDQ403107

Yugen Takegahara

Publication date: 29 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.03.017

zbMATH Keywords

representation ringBurnside ringtwisted group algebraMackey functorBrauer's induction theoremGreen functorplus constructiontwin functortwisted quantum double

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Frobenius induction, Burnside and representation rings (19A22) Twisted and skew group rings, crossed products (16S35) Projective representations and multipliers (20C25) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05)

Related Items

Tensor induction for \(M\)-Burnside rings ⋮ Lattice Burnside rings ⋮ Multiplicative induction and units for the ring of monomial representations

Cites Work

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• The crossed Burnside rings. III: The Dress construction for a Tambara functor
• Multiple Burnside rings and Brauer induction formulae
• The generalized Burnside ring of a finite group
• Generalized Burnside rings and group cohomology
• On the unit groups of Burnside rings
• Explicit Brauer induction
• A Tate cohomology sequence for generalized Burnside rings
• Structure of the Brauer ring of a field extension
• Idempotents of Burnside rings and Dress induction theorem
• The Brauer ring of a field
• Pointed groups and construction of modules
• Idempotent formula for the Burnside algebra with applications to the \(p\)-subgroup simplicial complex.
• Transformation groups and representation theory
• On G-functors. I: Transfer theorems for cohomological G-functors
• The equivalence of various generalizations of group rings and modules
• The representation theory of fully group-graded algebras
• A general theory of canonical induction formulae
• The \(p\)-blocks of the Mackey algebra
• Braided compact closed categories with applications to low dimensional topology
• Crossed Burnside rings. II: The Dress construction of a Green functor
• The ring of equivariant vector bundles on finite sets
• The representation ring of the quantum double of a finite group
• Crossed Burnside rings and Bouc's construction of Green functors
• Mackey functors, induction from restriction functors and coinduction from transfer functors
• The ring of monomial representations. I: Structure theory
• Axiomatic representation threory for finite groups
• On Artin's L-series with general group characters
• Group cohomology and gauge equivalence of some twisted quantum doubles
• The Representation Ring of the Twisted Quantum Double of a Finite Group
• Some remarks on G-functors and the Brauer morphism.
• TOPOLOGICAL QUANTUM FIELD THEORIES ASSOCIATED TO FINITE GROUPS AND CROSSED G-SETS
• Hochschild Constructions for Green Functors
• Beziehungen zwischen Klassenzahlen von Teilkörpern eines galoisschen Körpers. Herrn Professor Dr. Erhard Schmidt in dankbarer Verehrung zum 75. Geburtstag
• Quasi Hopf algebras, group cohomology and orbifold models
• Crossed Burnside rings. I: The fundamental theorem

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