We apply the diagram-technique formalism beyond the Hartree-Fock approximation to a two-dimensional nearly ideal electron gas in a weak perpendicular magnetic field. The case of an almost completely filled upper Landau level (filling factor ν0 < ∼ 1) with a quantum number N0 ≫ 1 is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where N 1/2 0 (1 −ν0) ≪ 1, these interactions lead to a splitting of the Landau levels. In the second regime, where N 1/2 0 (1 − ν0) ≫ 1, apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case N 1/2 0 (1−ν0) ≈ 1 cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes
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