HYPERKAHLER STRUCTURES WITH TORSION ON NILPOTENT LIE GROUPS

Using the classification by Dotti and Fino [3] we show the existence of an HKT metric on a neighbourhood of the centre of any 8-dimensional nilpotent Lie group G with invariant hypercomplex structure. This metric exists globally if the hypercomplex structure is abelian, and in these cases we construct an HKT structure on a neighbourhood of the zero section of the cotangent bundle T^*G extending the HKT metric on G.