The path group construction of Lie group extensions

Details The path group construction of Lie group extensions The path group construction of Lie group extensions

2007-03-12

arxiv.org/abs/math/0703342v2

J. Geom. and Phys. 58 (2008) 860-873

Mathematics

Differential Geometry

16 pages

Scientific paper

10.1016/j.geomphys.2008.02.006

We present an explicit realization of abelian extensions of infinite dimensional Lie groups using abelian extensions of path groups, by generalizing Mickelsson's approach to loop groups and the approach of Losev-Moore-Nekrasov-Shatashvili to current groups. We apply our method to coupled cocycles on current Lie algebras and to Lichnerowicz cocycles on the Lie algebra of divergence free vector fields.

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