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We perform the Lorentz-covariant non-Abelian gauging of supermembrane (M-2brane) action. This is a generalization of our previous work based onteleparallel formulation, in which Lorentz covariance was not manifest. Weintroduce the Killing supervector \xi^{A I} with the adjoint index I for anon-Abelian gauge group H. This formulation is applicable to thecompactification of supermembrane from eleven dimensions into D dimensions,such as H = SO(11-D) for the compactification M_{11} \to S^{11-D} \times M_D(1\le D \le 9).

Lorentz-Covariant Non-Abelian Gauging of Supermembrane