|Title: ||Classification of real solvable lie algebras whose simply connected lie groups have only zero or maximal dimensional coadjoint orbits
||Author(s): ||Le A.V.
||Keywords: ||K-orbit; MD(*, * - 1)-algebra; MD(*, 1)-algebra; MD-algebra
||Abstract: ||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.
||Issue Date: ||2015
||Publisher: ||Union Matematica Argentina
||Series/Report no.: ||Vol. 57, No. 2
|Appears in Collections:||INTERNATIONAL PUBLICATIONS|