Resumen de Classification of real solvable Lie algebras whose simply connected Lie groups have only zero or maximal dimensional coadjoint orbits

Ahn Vu Le, Van Hieu Ha, Ahn Tuan Nguyen, Tran Tu Hai Cao, Thi Mong Tuyen Nguyen

• We study a special subclass of real solvable Lie algebras having small dimensional or small codimensional derived ideals. It is well-known that the derived ideal of any Heisenberg Lie algebra is 1-dimensional and the derived ideal of the 4-dimensional real Diamond algebra is 1-codimensional. Moreover, all the coadjoint orbits of any Heisenberg Lie group as well as 4-dimensional real Diamond group are orbits of dimension zero or maximal dimension. In general, a (finite dimensional) real solvable Lie group is called an MD-group if its coadjoint orbits are zero-dimensional or maximal dimensional. The Lie algebra of an MD-group is called an MD-algebra and the class of all MD-algebras is called MD-class. Simulating the mentioned above characteristic of Heisenberg Lie algebras and 4-dimensional real Diamond algebra, we give a complete classification of MD-algebras having 1-dimensional or 1-codimensional derived ideals.