On the representations of 2-groups in Baez-Crans 2-vector spaces

Abstract

We study the theory of representations of a 2-group G in Baez-Crans 2-vector spaces over a field k of arbitrary characteristic, and the corresponding 2-vector spaces of intertwiners. We also characterize the irreducible and indecomposable representations. Finally, it is shown that when the 2-group is finite and the base field k is of characteristic zero or coprime to the orders of the homotopy groups of G, the theory essentially reduces to the theory of k-linear representations of the first homotopy group of G, the remaining homotopy invariants of G playing no role.