Neutrino - electron processes in a strong magnetic field and plasma

The total set of the neutrino - electron processes in a presence of both components of an active medium, hot dense plasma and strong magnetic field, is investigated for the first time. The contribution of the processes $\nu e^- \to \nu e^-$, $\nu e^+ \to \nu e^+$, $\nu \to \nu e^- e^+$, $\nu e^- e^+ \to \nu$ is shown to dominate and not to depend on the chemical potential of electron-positron gas. Relatively simple expressions for the probability and mean losses of the neutrino energy and momentum are obtained, which are suitable for a quantitative analysis.