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In this article，Lie symmetry of Nambu mechanical systems is discussed and its determining equations are established. Consequently，the structure equation and the associated conserved quantities are obtained. The inverse problem of Lie symmetries of the systems is also studied. As an example，Euler equations are used to illustrate the application of the main results.
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Keywords:
- Nambu mechanical systems /
- Lie symmetry /
- conserved quantities
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