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Am I missing something? what's the difference between $SL(2,C)$ (matrices 2x2 complex coefficients and determinant 1) and $PSL(2,C)$ which is isomorphic to $PGL(2,C)$ (matrices of complex coefficients with determinant 1)? Are $PSL(2,C)$ and $SL(2,C)$ the same?

J. W. Tanner
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Dac0
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    ok... I got the problem with taking in account only the determinant...., but I leave the question if someone made the same mistake – Dac0 Mar 19 '19 at 16:18
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    $PSL(2,\mathbb C) : = SL(2,\Bbb C)/{ \lambda \mathbb1 \mid \lambda\in \Bbb C^\times}$. Basically $PSL_2$ is $SL_2$ with the centre divided out. – s.harp Mar 19 '19 at 16:19
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    The $2\times2$ identity matrix $I$ and its negative $-I$ are two different elements of of $SL(2,C)$, but they represent the same element (equivalence class of matrices) in $PSL(2,C)$ and in $PGL(2,C)$. – Andreas Blass Mar 19 '19 at 19:22

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