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http://dx.doi.org/10.4134/CKMS.c210308

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)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1181-1197 More about this Journal
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
MD-algebras; coadjoint orbits; classification of Lie group;
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