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关键词： Generalized complex structures   Generalized Kahler structures   Lie groups   Lie algebras   Dolbeault cohomology   Bott-Chern cohomology   Aeppli cohomology  

摘要： We give a complete classification of left invariant generalized complex structures of type 1 on four dimensional simply connected Lie groups and we compute for each class its invariant generalized Dolbeault cohomology, its invariant generalized Bott-Chern cohomology and its invariant generalized Aeppli cohomology. We classify also left invariant generalized Kahler structures on four dimensional simply connected Lie groups. (C) 2021 Elsevier Inc. All rights reserved.