  We lift an action of a torus $\mathbb{T}^n$ on the spectrum of a continuous
trace algebra to an action of a certain crossed module of Lie groups that is an
extension of $\mathbb{R}^n$. We compute equivariant Brauer and Picard groups
for this crossed module and describe the obstruction to the existence of an
action of $\mathbb{R}^n$ in our framework.
