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

P. B. Kronheimer
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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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P. B. Kronheimer. 2004-09-15. A hyperkahler structure on the cotangent bundle of a complex Lie group. https://arxiv.org/abs/math/0409253

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