# Definition The [[Special Linear Group in Two Complex Dimensions]] $SL(2,\mathbb{C})$ is the double cover of the [[Restricted Lorentz Group in 4 Dimensions]] $SO(3,1)_o$. This means that there is a two-to-one (double) and onto (cover) [[group homomorphism|homomorphism]] from the former to the latter. Moreover, their Lie algebras are [[Lie Algebra Isomorphism|isomorphic]], i.e., $\mathfrak{so}(3,1) \cong \mathfrak{sl}(2,\mathbb{C})_\mathbb{R}$ The situation is analogous to the [[Relationship Between SO(3) and SU(2)]], which is discussed extensively on that page.