Topic
Burnside ring
About: Burnside ring is a research topic. Over the lifetime, 303 publications have been published within this topic receiving 3035 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1979
TL;DR: The Burnside ring of finite G-sets has been studied in this paper for the purpose of proving equivariant homology and cohomology of stable G-vector bundles.
Abstract: The Burnside ring of finite G-sets.- The J-homomorphism and quadratic forms.- ?-rings.- Permutation representations.- The Burnside-ring of a compact Lie group.- Induction theory.- Equivariant homology and cohomology.- Equivariant homotopy theory.- Homotopy equivalent group representations.- Geometric modules over the Burnside ring.- Homotopy-equivalent stable G-vector bundles.
474 citations
TL;DR: The Burnside ring of G is a semisimpleteness algebra over Q and formulas for certain primitive idempotents of this algebra yield the theorem of Artin on rational characters.
131 citations
TL;DR: In this article, it was shown that the group D(P) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group, and that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P.
Abstract: The group D(P) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P. We also obtain partial results on its torsion subgroup. We determine next the structure of Q\otimes D(-) viewed as a functor, which turns out to be a simple functor S_{E,Q}, indexed by the elementary group E of order p^2 and the trivial Out(E)-module Q. Finally we describe a rather strange exact sequence relating Q\otimes D(P), Q\otimes B(P), and Q\otimes R(P), where B(P) is the Burnside ring and R(P) is the Grothendieck ring of QP-modules.
78 citations
63 citations
TL;DR: In this paper, it was shown that well-known product decompositions of formal power series arise from combinatorially defined canonical isomorphisms between the Burnside ring of the infinite cyclic group on the one hand and Grothendieck's ring of formal series with constant term 1 as well as the universal ring of Witt vectors on the other hand.
62 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 8 |
| 2020 | 16 |
| 2019 | 22 |
| 2018 | 20 |
| 2017 | 17 |
| 2016 | 10 |