Abstract
One of the most profound results in the theory of Lie algebras states that any two Cartan subalgebras of a finite-dimensional Lie algebra over an algebraically closed field of characteristic 0 are conjugate relative to the group of special automorphisms generated by the exponents of nilpotent inner derivations. Using some new ideas, we prove an analog of this statement for n-ary n-Lie algebras. Other interesting properties of Cartan algebras, which are known to be shared by Lie algebras, are carried over to n-Lie algebras.
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