  Numerical simulations of kinetic problems can become prohibitively expensive
due to their large memory footprint and computational costs. A method that has
proven to successfully reduce these costs is the dynamical low-rank
approximation (DLRA). One key question when using DLRA methods is the
construction of robust time integrators that preserve the invariances and
associated conservation laws of the original problem. In this work, we
demonstrate that the augmented basis update & Galerkin integrator (BUG)
preserves solution invariances and the associated conservation laws when using
a conservative truncation step and an appropriate time and space
discretization. We present numerical comparisons to existing conservative
integrators and discuss advantages and disadvantages
