Some radicals, Frattini and Cartan Subalgebras of Leibniz n-algebras
Felipe GagoDepartamento de Álgebra , Universidad de Santiago de Compostela , 15782 Santiago de Compostela , SpainM. LadraBakhrom Omirov : Institute of Mathematics and Information Technologies , 29, Dormon Yoli , 100125 Tashkent , UzbekistanB. A. OmirovDepartment of Mathematics , National University of Uzbekistan , Vuz- gorogok , 27 , 100174 Tashkent , UzbekistanRustam TurdibaevDepartamento de Álgebra , Universidad de Santiago de Compostela , 15782 Santiago de Compostela , Spain
2011en
ABI
Annotatsiya
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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