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

• Ahn Vu Le ^[2] ; Van Hieu Ha ^[2] ; Ahn Tuan Nguyen ^[3] ; Tran Tu Hai Cao ^[4] ; Thi Mong Tuyen Nguyen ^[1]
  1. [1] Dong Thap University

     Dong Thap University

     Vietnam

     
  2. [2] Vietnam National University, Vietnam
  3. [3] University of Physical Education and Sports, Vietnam
  4. [4] Le Quy Don High School for the Gifted, Vietnam

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 57, Nº. 2, 2016, págs. 119-143
• Idioma: inglés
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• Resumen

  • 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.