Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals

2011/01/11 by Le Anh Vu, Vu, Le Anh, Ha Van Hieu +3
Mathematics · #20C20 #F.2.2 #FOS: Mathematics #Primary 22E45 #Representation Theory (math.RT) #Secondary 46E25 #acm:20C20 #acm:22E45 #acm:46E25 #math.RT #msc:20C20 #msc:22E45 #msc:46E25

paper · pdf · doi:10.48550/arxiv.1101.2181

9 pages, no figures

arxiv created 2012/02/09 · arxiv updated 2012/02/10

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-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.

Related

• Classification of 5-dimensional MD-algebras having commutive derived ideals
• On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal
• Classification of Real Solvable Lie Algebras Whose Simply Connected Lie Groups Have Only Zero or Maximal Dimensional Coadjoint Orbits
• Classification of Solvable Lie algebras whose non-trivial Coadjoint Orbits of simply connected Lie groups are all of Codimension 2
• Classification of a Class of Solvable Real Lie Algebras by using Techniques in Matrix Theory