A hyperkahler structure on the cotangent bundle of a complex Lie group
Differential Geometry
2007-05-23 v1 Symplectic Geometry
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.
Cite
@article{arxiv.math/0409253,
title = {A hyperkahler structure on the cotangent bundle of a complex Lie group},
author = {P. B. Kronheimer},
journal= {arXiv preprint arXiv:math/0409253},
year = {2007}
}
Comments
This paper was originally written in 1988 but not published. It is being made available now in electronic form