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

By P. Kronheimer. 2004

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/20b981a5e92468cc937948e39c92a6d940abbae8