nLab automorphism Lie group

The automorphism group Aut(G)Aut(G) of a Lie group GG itself canonically inherits the structure of a Lie group. Its Lie algebra is the derivation Lie algebra of the Lie algebra 𝔤\mathfrak{g} of GG: Lie(Aut(G))𝔡𝔢𝔯(𝔤)Lie(Aut(G)) \simeq \mathfrak{der}(\mathfrak{g}).

Created on March 7, 2017 at 09:59:41. See the history of this page for a list of all contributions to it.