2-Groups, 2-Characters, and Burnside Rings

Dmitriy Rumynin; Alex Wendland

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arXiv · 1604.02926

2-Groups, 2-Characters, and Burnside Rings

Dmitriy Rumynin·Alex Wendland

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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.

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BibTeX RIS

Dmitriy Rumynin, Alex Wendland. 2018-05-03. 2-Groups, 2-Characters, and Burnside Rings. https://arxiv.org/abs/1604.02926

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