On the Basis of the Burnside Ring of a Fusion System

2014/03/24 by Gelvin, Matthew, Reeh, Sune Precht, Yalcin, Ergun
#19A22) #20D20 (20J15 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1403.6053

Abstract

We consider the Burnside ring A(F) of F-stable S-sets for a saturated fusion system F defined on a p-group S. It is shown by S. P. Reeh that the monoid of F-stable sets is a free commutative monoid with canonical basis \α_P\. We give an explicit formula that describes α_P as an S-set. In the formula we use a combinatorial concept called broken chains which we introduce to understand inverses of modified Möbius functions.

Related

• The abelian monoid of fusion-stable finite sets is free
• Burnside Rings of Fusions Systems and their Unit Groups
• Prime ideals of the Burnside ring of a saturated fusion system
• A Burnside ring for monoids
• Uniqueness of factorization for fusion-invariant representations