Yet another construction of the central extension of the loop group

2001/01/31 by Michael K. Murray, Daniel Stevenson, Murray, Michael K. +1
Mathematics · #22E67 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E67

paper · pdf · doi:10.48550/arxiv.math/0101258

Conference talk at the National Research Symposium on Geometric Analysis and Applications at the Centre for Mathematics and its Applications

arxiv created 2001/01/31 · arxiv updated 2009/11/30

Abstract

We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop group.

Related

• The Kac-Moody central extension on a loop group in the seven-term exact sequence
• Central Extensions of Gauge Groups Revisited
• Lie 2-groups from loop group extensions
• From Loop Groups to 2-Groups
• Central leaves in loop groups