2016/04/11 by Rumynin, Dmitriy, Wendland, Alex
#18D05 (Primary) #19A22 (Secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1604.02926
We study 2-representations, i.e., actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno formula for the Ganter-Kapranov 2-character of a finite group.