I have had a lot of trouble to be able to solve the following problem:
Show that $SU (2, \mathbb{C})$ is homeomorphic to the unit sphere $\mathbb{S}^
3 = \{x = (x_1, x_2, x_3, x_4) \in \mathbb{R}^4:||x|| = 1\}$.
Note $SU (2, \mathbb{C})$ Is the group of unit matrices $A$ of $2 × 2$ with coefficients in $\mathbb{C}$,
such that $A^∗ = A^{−1}$
, here $A^∗$ denotes the conjugate matrix transposed of $A$. We highlight
that ||·|| denotes the standard Euclidean norm.
somebody could help me?
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What did you try? – José Carlos Santos May 31 '21 at 07:41
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look for a function that sends me from the matrices to S ^ 3 but at the time of giving homeomorphism I could not do it – Emmanuel Uh Pat May 31 '21 at 07:48