Recall that a Lie group is a smooth maniford $G$ together with structure of a group such that the group operations $$\mu:Gimes G\rightarrow G,\;\;(g_1,g_2)\rightarrow g_1\cdot g_2$$ $$i:G\rightarrow G,\;\;g\rightarrow g^{-1}$$ are smooth mappings.