A hyperkahler structure on the cotangent bundle of a complex Lie group

2004/09/15 by P. B. Kronheimer, Kronheimer, P. B. · 1 citation
Mathematics · #53C26 (Primary) 53C28 #53D30 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53C26 #msc:53C28 #msc:53D30

paper · pdf · doi:10.48550/arxiv.math/0409253

This paper was originally written in 1988 but not published. It is being made available now in electronic form

arxiv created 2004/09/15 · arxiv updated 2009/12/01

Abstract

Let G be compact Lie group. It is shown that the cotangent bundle of the complexification of G admits a hyperkahler structure which is invariant under left and right translations by elements of G. The proof is to realize the cotangent bundle of the complex group as a moduli space of solutions to Nahm's equations on the closed interval.

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