Exercise [18.01]

Pibe · 06 Jul 2009, 20:15

Hi again.

I don't know if i understood this excersise. Here is my solution:

$C_0:\mathbb{CE}^4 \longrightarrow \mathbb{E}^4$
$(\omega,\xi,\eta,\zeta) \longrightarrow \frac{1}{2}(\omega+\overline{\omega},\xi+\overline{\xi},\eta+\overline{\eta},\zeta+\overline{\zeta})$

$C_1:\mathbb{CE}^4 \longrightarrow \mathbb{M}$
$(\omega,\xi,\eta,\zeta) \longrightarrow \frac{1}{2}(\omega+\overline{\omega},\xi-\overline{\xi},\eta-\overline{\eta},\zeta-\overline{\zeta})$

$C_2:\mathbb{CE}^4 \longrightarrow \mathbb{\widetilde{M}}$
$(\omega,\xi,\eta,\zeta) \longrightarrow \frac{1}{2}(\omega-\overline{\omega},\xi+\overline{\xi},\eta+\overline{\eta},\zeta+\overline{\zeta})$

Are these mappings the answer to the excersise?
I think these mappings aren't involutory...but I didn't find another answer...
Can anybody clarify this question?

See you soon!!