2-Groups, 2-Characters, and Burnside Rings
Category Theory
2018-05-04 v4 Algebraic Topology
K-Theory and Homology
Representation Theory
Abstract
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.
Cite
@article{arxiv.1604.02926,
title = {2-Groups, 2-Characters, and Burnside Rings},
author = {Dmitriy Rumynin and Alex Wendland},
journal= {arXiv preprint arXiv:1604.02926},
year = {2018}
}
Comments
Version 2: minor corrections. Version 3: major revisions of the first half of the paper. Version 4: minor corrections