Urs Schreiber

2005-04-07 10:02:30 UTC

We have a new preprint

J. Baez, A. Crans, U. Schreiber & D. Stevenson

http://golem.ph.utexas.edu/string/archives/000547.html .

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

String(n).

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.

J. Baez, A. Crans, U. Schreiber & D. Stevenson

From Loop Groups to 2-Groups,

math.QA/0504123http://golem.ph.utexas.edu/string/archives/000547.html .

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

String(n).

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.