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

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

2011-03-14

arxiv.org/abs/1103.2725v1

Mathematics

Rings and Algebras

16 pages

Scientific paper

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 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.

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