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We give a complete classification of left invariant generalized complexstructures of type 1 on four dimensional simply connected Lie groups and wecompute for each class its invariant generalized Dolbeault cohomology, itsinvariant generalized Bott-Chern cohomology and its invariant generalizedAeppli cohomology. We classify also left invariant generalized K\"ahlerstructures on four dimensional simply connected Lie groups.

Left invariant generalized complex and K\"ahler structures on simply  connected four dimensional Lie groups: classification and invariant  cohomologies