  A dynamical symmetry is employed to determine the structure of the quantum
non-Markovian time-local master equation. Such a structure is composed from two
components: scalar kinetic coefficients and the standard quantum Markovian
operator form. The kinetic coefficients are generally time-dependent and
incorporate information on the kinematics and memory effects, while the
operators manifest the dynamical symmetry. Specifically, we focus on
time-translation symmetric dynamics, where the Lindblad jump operators
constitute the eigenoperators of the free dynamics. This symmetry is motivated
by thermodynamic microscopic considerations, where strict energy conservation
between system and environment imposes the time-translation symmetry. The
construction is generalized to other symmetries, and to driven quantum systems.
The formalism is illustrated by three exactly solvable non-Markovian models,
where the exact reduced description exhibits a dynamical symmetric structure.
The formal structure of the master equation leads to a first principle
calculation of the exact kinetic coefficients. This opens the possibility to
simulate in a modular fashion non-Markovian dynamics.
