The openness condition for a coadjoint orbit projection of the semidirect product Lie group M((n, p), ℝ) ⋊ GL (n, ℝ)

Let G(n, p) be the semidirect product Lie group of the vector space K : = M(( n,p ),ℝ) of n × p real matrices and the Lie group L : = GL( n ,ℝ) of n × n real invertible matrices. Moreover, we denote by g( n, p ) the Lie algebra of G ( n, p ) whose the dual vector space is g* ( p, n ). In this paper,...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. Conference series 2021-05, Vol.1872 (1), p.12017
Main Author: Kurniadi, E
Format: Article
Language:English
Subjects:
Group theory
Lie groups
Mathematical analysis
Matrix algebra
Matrix methods
Orbits
Physics
Projection
Vector space
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let G(n, p) be the semidirect product Lie group of the vector space K : = M(( n,p ),ℝ) of n × p real matrices and the Lie group L : = GL( n ,ℝ) of n × n real invertible matrices. Moreover, we denote by g( n, p ) the Lie algebra of G ( n, p ) whose the dual vector space is g* ( p, n ). In this paper, we study the projection of a coadjoint orbit of G ( n, p ) from g* ( p, n ) to K *. The main purpose is to give necessary and sufficient conditions for the openness of a coadjoint orbit projection. In this research, we applied the study literature method by studying the openness of a coadjoint orbits. As the main result, we proved the openness condition for coadjoint orbits projections in K *. For the future research, the openness of coadjoint orbits of G ( n, p ) still needs to be investigated more.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1872/1/012017