In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Isomorphic Lie groups have isomorphic Lie algebras but the converse is not necessarily true. One obvious counter example is and which are non-isomorphic as Lie groups but their Lie algebras are isomorphic. However, by restricting our attention to the simply connected Lie groups, the Lie group-Lie algebra correspondence will be one-to-one.