Communications of the
Korean Mathematical Society CKMS

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: MD-algebras, coadjoint orbits, classification of Lie group

MSC numbers: Primary 17B08, 17B30

Supported by: 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. 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.