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CLASSIFICATION OF SOLVABLE LIE GROUPS WHOSE NON-TRIVIAL COADJOINT ORBITS ARE OF CODIMENSION 1
Ha, Hieu Van,Hoa, Duong Quang,Le, Vu Anh Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4
We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.
Hieu Van Ha,Vu Anh Le,Tu Thi Cam Nguyen,Hoa Duong Quang 대한수학회 2023 대한수학회지 Vol.60 No.4
We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding to simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of MD-algebras.