A 2-group construction from an extension of the 3-loop group Ω^3G
Abstract
We define a 3-loop group Ω^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 Ω^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.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- December 2019
- DOI:
- 10.1007/s11005-019-01201-y
- arXiv:
- arXiv:1810.00230
- Bibcode:
- 2019LMaPh.109.2649M
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematical Physics;
- 22E67;
- 81R10;
- 18D35;
- 22A22
- E-Print:
- 13 pages