Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF SOLVABLE LIE GROUPS WHOSE NON-TRIVIAL COADJOINT ORBITS ARE OF CODIMENSION 1

  • Ha, Hieu Van (Faculty of Economic Mathematics University of Economics and Law and Vietnam National University) ;
  • Hoa, Duong Quang (Department of Mathematics Hoa Sen University) ;
  • Le, Vu Anh (Faculty of Economic Mathematics University of Economics and Law and Vietnam National University)
  • Received : 2021.09.16
  • Accepted : 2022.02.08
  • Published : 2022.10.01
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Abstract

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.

Keywords

Acknowledgement

This research is funded by University of Economics and Law, Vietnam National University Ho Chi Minh City/VNU-HCM, under grant number CS/2020-08. The first author would like to express his deep gratitude to his wife, Thuy Nguyen Thanh, for her encouragement and support.

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