= Complex special linear group in dimension two
{title2=$SL(2,\mathbb C)$}
= SL(2,C)
{c}
{synonym}
Complex two-by-two <matrices> of <determinant> one form a complex three-dimensional <Lie group>, or a real six-dimensional <Lie group>. Their congruence action on Hermitian two-by-two <matrices> gives the <Lorentz spinor double cover> with kernel $\{I,-I\}$. The two <Weyl spinor> representations are $A$ and $(A^\dagger)^{-1}$. Treating the group as real is essential for the second, antiholomorphic representation.
Back to article page
