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Let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation F with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation F . We classify such structures J which are almost Kähler (AK), integrable (I) or Kähler (K). Hereby we construct several new multi-dimensional examples in each class.
