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Is $PGL(n,\Bbb{R}) \cong SL(n+1, \Bbb{R})$ for even n?
Is the following claim correct?
Claim: If n is even, $PGL(n,\Bbb{R}) \cong SL(n+1, \Bbb{R})$.
Proof:
Recall $PGL(n,\Bbb{R}) \cong GL(n+1, \Bbb{R})/Z$, where $Z = \{M | M=\alpha I, \alpha \in \Bbb{...
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