Plasma influence on the neutrino - electron processes in a strong magnetic field

An influence of the magnetized electron - positron plasma on the absorption and loss of the energy and momentum in a process of neutrino propagation is investigated. A total contribution of all crossed processes, $\nu \to \nu e^- e^+$, $\nu e^- \to \nu e^-$, $\nu e^+ \to \nu e^+$, $\nu e^- e^+ \to \nu$, is found for the first time, which appears 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.