\(q\)-deformation of Witt-Burnside rings

DOI10.1007/s00209-007-0119-2zbMath1152.19001arXivmath/0411353OpenAlexW2114940048MaRDI QIDQ2384743

Young-Tak Oh

Publication date: 10 October 2007

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

Full work available at URL: https://arxiv.org/abs/math/0411353

zbMATH Keywords

Witt vectorsWitt-Burnside ringnecklace ringBurnside-Grothendieck ring

Mathematics Subject Classification ID

Related Items (11)

Decomposition of the Witt-Burnside ring and Burnside ring of an abelian profinite group ⋮ Nested Witt vectors and their \(q\)-deformation ⋮ Classification of the ring of Witt vectors and the necklace ring associated with the formal group law \(X+Y - qXY\) ⋮ Group-theoretical generalization of necklace polynomials ⋮ Witt-Burnside functor attached to \(\boldsymbol{Z}_p^2\) and \(p\)-adic Lipschitz continuous functions ⋮ \(q\)-analog of the Möbius function and the cyclotomic identity associated to a profinite group. ⋮ \(q\)-deformed necklace rings and \(q\)-Möbius function ⋮ A WITT–BURNSIDE RING ATTACHED TO A PRO-DIHEDRAL GROUP ⋮ Witt-Burnside ring and Burnside ring over a special \(\lambda \)-ring ⋮ Necklace rings and logarithmic functions ⋮ Generalized Burnside--Grothendieck ring functor and aperiodic ring functor associated with profinite groups

Cites Work

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• The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, \(\lambda\)-rings, and the universal ring of Witt vectors
• The Burnside ring of profinite groups and the Witt vector construction
• \(R\)-analogue of the Burnside ring of profinite groups and free Lie algebras
• \(\lambda\)-rings and the representation theory of the symmetric group
• Witt vectors and the algebra of necklaces
• Transformation groups and representation theory
• Cohomology of modules in the principal block of a finite group
• Formal group-theoretic generalizations of the necklace algebra, including a \(q\)-deformation
• A functorial property of nested Witt vectors
• Necklace rings and logarithmic functions
• Generalized Burnside--Grothendieck ring functor and aperiodic ring functor associated with profinite groups

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