K-orbits of solvable Lie groups whose Lie algebras are 7-dimensional corresponding to 5-dimensional nilradicals
Main Article Content
Abstract
Kirillov’s orbit method is an important tool in the study of representations of Lie groups and Lie algebras, in which the coadjoint orbits play a central role. This paper investigates the geometric structure of the coadjoint orbits of simply connected solvable Lie groups whose corresponding Lie algebras are given. Based on the recent classification results of a special class of 7-dimensional solvable Lie algebras with 5-dimensional nilradicals, the paper presents a visualization of the geometric picture of the coadjoint orbits of those simply connected solvable Lie groups corresponding to the class of 7-dimensional solvable Lie algebras.