Armenian Journal of Mathematics, 16(1)
2024; 1–28
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The Geometry of the Projective Action of SL ( 3 , R ) from the Erlangen Perspective

Debapriya Biswas*, Ipsita Rajwar

Received: 2024-12-03 · Published: 2024-01-11

© 2024 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
The Geometry of the Projective Action of SL ( 3 , R ) from the Erlangen Perspective
Authors
Debapriya Biswas, Ipsita Rajwar
Source journal
Armenian Journal of Mathematics, 16(1)
Published
2024-01-11
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2024.16.1-1-28

Abstract

In this paper, we have investigated the projective action of the Lie group SL(3,R)SL(3,R) on the homogeneous space RP2RP2. In particular, we have studied the action of the subgroups of  SL(3,R)SL(3,R) on the non-degenerate conics in the space RP2RP2. Using the Iwasawa decomposition of SL(2,R)SL(2,R), we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to  PSL(2,R)PSL(2,R) under certain conditions.
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