The Kac-Moody central extension on a loop group in the seven-term exact sequence

2018/10/28 by Fujitani, T.
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1810.12755

Abstract

Mickelsson defined a group 2-cocycle on the group of smooth maps from the closed unit 2-disk to a Lie group G and constructed a smooth central extension on a loop group of G, called the affine Kac-Moody central extension. We reformulate this central extension theory in the terms of the seven-term exact sequence for cohomology groups for discrete groups.

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• A seven-term exact sequence for the cohomology of a group extension
• Yet another construction of the central extension of the loop group
• A higher Kac-Moody extension for two-dimensional gauge groups
• Infinite loop spaces associated to affine Kac-Moody groups
• From Loop Groups to 2-Groups