I'm halfway through a question on a past differential geometry exam, and suddenly in comes a matrix g a member of SL(2,C) (where C denotes the complex numbers)(adsbygoogle = window.adsbygoogle || []).push({});

Now, I can't remember how to express a general element of this group: I know the matrix must be

[tex]\left(\begin{array}{cc}a&b\\c&d\end{array}\right)[/tex] such that ad-bc=1, but can this be expressed in a more precise way in the complex case (i.e. with fewer than four unknowns, maybe by utilising the complex conjugate)?

I've tried looking on the internet, but to no avail. I would really appreciate someone helping, since I could do with getting on with the question!

Thanks in advance!

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# Homework Help: General element of SL(2,C)

**Physics Forums | Science Articles, Homework Help, Discussion**