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

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

2004-09-15

arxiv.org/abs/math/0409253v1

Mathematics

Differential Geometry

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

Scientific paper

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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