Special linear group:SL(2,C)

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Definition

The group $SL(2,\mathbb {C} )$ is defined as the group of $2\times 2$ matrices with entries from the field of complex numbers and determinant $1$, under matrix multiplication.

$SL(2,\mathbb {C} ):=\left\{{\begin{pmatrix}a&b\\c&d\\\end{pmatrix}}\mid a,b,c,d\in \mathbb {C} ,ad-bc=1\right\}$.

It is a particular case of a special linear group over complex numbers, member of family:special linear group of degree two, and hence of a special linear group.

Elements

Further information: element structure of special linear group:SL(2,C)