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Register a new userCartan Subalgebras of Leibniz $n$-Algebras
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The present paper is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz $n$-algebras. The relationship between Cartan subalgebras and regular elements of given Leibniz $n$-algebra and Cartan subalgebras and regular elements of the corresponding factor $n$-Lie algebra is established.
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In this paper we initiate the study of the maximal subalgebras of exceptional simple classical Lie algebras g over algebraically closed fields k of positive characteristic p, such that the prime characteristic is good for g. In this paper we deal with what is surely the most unnatural case; that is, where the maximal subalgebra in question is a simple subalgebra of non-classical type. We show that only the first Witt algebra can occur as a subalgebra of g and give explicit details on when it may be maximal in g.
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We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself.
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