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

Original · EN

In the present work we introduce notions such as k-solvability, s- and K₁-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 that 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.