Geodesic
Geometric Invariants Under the Möbius Action of the Group $SL(2;\mathbb R)$
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 925 .

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In this paper we have introduced new invariant geometric objects in the homogeneous spaces of complex, dual and double numbers for the principal group $SL(2;\mathbb{R})$, in the Klein's Erlangen Program. We have considered the action as the Möbius action and have taken the spaces as the spaces of complex, dual and double numbers. Some new decompositions of $SL(2;\mathbb{R})$ have been used.
Classification : 57S20, 57S25, 51H20, 14R20, 22F30, 54H11
Keywords: Lie group, $SL(2;\mathbb R)$ group, invariants, Möbius transformation, homogeneous spaces, Iwasawa decomposition 
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     author = {Debapriya Biswas and Sandipan Dutta},
     title = {Geometric {Invariants} {Under} the {M\"obius} {Action} of the {Group} $SL(2;\mathbb R)$},
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Debapriya Biswas; Sandipan Dutta. Geometric Invariants Under the Möbius Action of the Group $SL(2;\mathbb R)$. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 925 . http://geodesic.mathdoc.fr/item/KJM_2021_45_6_a6/