Appendix B of “Differential Geometry of Toda-Type Systems.” Lie Algebras, Geometry, and Toda-Type Systems, 1997, pp. 129–207., https://doi.org/10.1017/cbo9780511599927.004, states that
"...the connected component of the group $\text{Aut}(\mathfrak{g})$" containing unity, which, for the considered case of a semisimple Lie algebra, coincides with the Lie group $\text{Int}(\mathfrak{g})$ of internal automorphisms of $\mathfrak{g}$.",
whereas I failed to find materials supporting this fact. Any idea on how to prove this or related articles or books? THX :)
In fact, the Lie algebra of $\text{Aut}(\mathfrak{g})$ is $\text{Der}\mathfrak{g}$, which, given that $\mathfrak{g}$ is semisimple, is $\text{ad}\mathfrak{g}$. Note that $\text{Int}(\mathfrak{g})$ is the Lie group correponding to $\text{ad}\mathfrak{g}$, which is suffice to prove the proposition.