Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program

Debapriya Biswas; Ipsita Rajwar

doi:10.52737/18291163-2022.14.11-1-15

Authors

Debapriya Biswas Indian Institute of Technology Kharagpur
Ipsita Rajwar Indian Institute of Technology Kharagpur

DOI:

https://doi.org/10.52737/18291163-2022.14.11-1-15

Keywords:

Lie Group $\text{SL}(3,\mathbb{R})$, Homogeneous Space, Iwasawa Decomposition, One-Parameter Subgroups, Group Action, Derived Representation, Orbit, Curvature, Fixed Point

Abstract

We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.

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