On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal

2006/03/03 by Le Anh Vu, Vu, Le Anh
Mathematics · #20C20 #FOS: Mathematics #Primary 22E45 #Representation Theory (math.RT) #Secondary 46E25 #math.RT #msc:20C20 #msc:22E45 #msc:46E25

paper · pdf · doi:10.48550/arxiv.math/0603076

14 pages, no figure

arxiv created 2006/03/03 · arxiv updated 2009/12/01

Abstract

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras G with the derived ideal G¹ := [G, G] is a 3-dimensional commutative Lie algebra.

Related

• Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals
• Classification of 5-dimensional MD-algebras having commutive derived ideals
• Classification of Real Solvable Lie Algebras Whose Simply Connected Lie Groups Have Only Zero or Maximal Dimensional Coadjoint Orbits
• The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits
• Representation of Real Solvable Lie Algebras Having 2-dimensional Derived Ideal and Geometry of Coadjoint Orbits of Corresponding Lie Groups