Some radicals, Frattini and Cartan subalgebras of Leibniz n-algebras

In the present work, we introduce notions such as k-solvability, s- and K-1-nilpotency and the corresponding radicals. We prove that these radicals are invariant under derivations of Leibniz n-algebras. The Frattini and Cartan subalgebras of Leibniz n-algebras are studied. In particular, we construct examples that show a classical result on conjugacy of Cartan subalgebras of Lie algebras, which also holds in Leibniz algebras and Lie n-algebras, is not true for Leibniz n-algebras.