2005-04-07 10:02:30 UTC
J. Baez, A. Crans, U. Schreiber & D. Stevenson
From Loop Groups to 2-Groups,math.QA/0504123
It proves the following two theorems:
1) The weak Lie 2-algebras g_k defined in HDA6 are equivalent to
infinite-dimensional strict Fréchet Lie 2-algebras P_k g. These are related
to the Kac-Moody central extension ?_k g of the loop algebra ? g and come
from infinite-dimensional Fréchet Lie 2-groups Omega_k G.
2) The nerve |P_k G| of P_k G is, for G=Spin(n), the topological group
Hence 2-bundles and gerbes with structure 2-group P_k G should be related to
"String(n)-bundles" and 2-connections on them possibly to the enriched
elliptic objects defined by Stolz and Teichner.