Generalised Burnside Rings, G-categories and Module Categories

2011/10/21 by Paul E. Gunnells, Gunnells, Paul, Andrew Rose +3
Mathematics · #19A22 (Primary) 20F55 (Secondary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1110.4722

openalex publication_date 2011/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This note describes an application of the theory of generalised Burnside rings to algebraic representation theory. Tables of marks are given explicitly for the groups S₄ and S₅ which are of particular interest in the context of reductive algebraic groups. As an application, the base sets for the nilpotent element F₄ (a₃) are computed.

Citations

• Geometric Representation Theory of Restricted Lie Algebras of Classical Type
• Group-graded rings, smash products, and group actions

Related

• The extended Burnside ring and module categories
• The Burnside ring of simple C-sets
• Explicit Generators for the Unit Group of the Burnside ring
• Simplicial Burnside ring
• A note on the lambda-structure on the Burnside ring