Explicit Formulas for 2-Characters

TL;DR

This paper provides explicit formulas for 2-characters associated with 2-representations of finite groups, linking them to cohomological data, and explores their implications.

Contribution

It introduces explicit formulas for 2-characters in terms of cohomological data, advancing the understanding of 2-representations in 2-vector spaces.

Findings

Explicit formulas for 2-characters derived from cohomological data

Connections established between 2-characters and cohomology

Consequences for the theory of 2-representations

Abstract

Ganter and Kapranov associated a 2-character to 2-representations of a finite group. Elgueta classified 2-representations in the category of 2-vector spaces 2Vect_k in terms of cohomological data. We give an explicit formula for the 2-character in terms of this cohomological data and derive some consequences.