A 2-group construction from an extension of the 3-loop group varOmega ^3G

Abstract

We define a 3-loop group {varOmega ^3G} as a subgroup of smooth maps from a 3-ball to a Lie group G, and then construct a 2-group based on an automorphic action on the Mickelsson–Faddeev extension of {varOmega ^3G}. In this, we follow the strategy of Murray et al. (J Lie Theory 27(4):1151–1177, 2017), who earlier described a similar construction for one-dimensional loops. The three-dimensional situation presented here is further complicated by the fact that the 3-loop group extension is not central.