Some radicals, Frattini and Cartan subalgebras of Leibniz<i>n</i>-algebras
Felipe GagoDepartment of Algebra, University of Santiago de Compostela, Santiago de Compostela, SpainM. LadraDepartment of Algebra, University of Santiago de Compostela, Santiago de Compostela, SpainB. A. OmirovInstitute of Mathematics, National University of Uzbekistan, Tashkent, UzbekistanRustam TurdibaevInstitute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Аннотация
In the present work, we introduce notions such as -solvability, - and -nilpotency and the corresponding radicals. We prove that these radicals are invariant under derivations of Leibniz -algebras. The Frattini and Cartan subalgebras of Leibniz -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 -algebras, is not true for Leibniz -algebras.
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