I know that every Lie group is orientable. I want to know whether there is a standard choice of orientation.
The standard orientation on $\mathbb{R}^n$ is $\left( {\partial \over \partial x_1}, \ldots, {\partial \over \partial x_n} \right)$. For example, what is the standard orientation on $\mathrm{SO}(n)$?
Thank you.