Let R be a prime ring of characteristic not 2, L nonzero square closed Lie ideal and let F : → R, G generalized derivations associated with d g respectively. In this paper, we study several conditions that imply the is central. Moreover, it shown assumption primeness can removed.

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such algebra g, we describe space structures on g up to isomorphism. As an application, having non-trivial abelian J-invariant ideal are classified dimensions.

If a Lie algebra g can be generated by M of its elements E1, . . . , EM , and if any other Lie algebra generated by M other elements F1, . . . , FM is a homomorphic image of g under the map Ei → Fi, we say that it is the free Lie algebra on M generators. The free nilpotent Lie algebra gM,r on M generators of rank r is the quotient of the free Lie algebra by the ideal gr+1 generated as follows: ...

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　The attempt to find out if someone is telling a lie has been of human's interest. One of the techniques which is believed to be efficient in future is fMRI (functional Magnetic Resonance Imaging), using which the changes of regional blood flow during the designed paradigm can be recorded. This method has been considered as a better technique for studying lie and deception. For investigating th...

In this note we study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F ). AMS classification: 17B50

Some locally finite simple Lie algebras are graded by finite (possibly nonreduced) root systems. Many more algebras are sufficiently close to being root graded that they still can be handled by the techniques from that area. In this paper we single out such Lie algebras, describe them, and suggest some applications of such descriptions.

We study a class of positively graded Lie algebras with a pattern of homogeneous components similar to that of the graded Lie algebra associated to the Nottingham group with respect to its lower central series.

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibn...