The concept of (α, β)-fuzzy Lie algebras over an (α, β)-fuzzy field is introduced. We provide characterizations of an (∈,∈ ∨q)-fuzzy Lie algebra over an (∈,∈ ∨q)-fuzzy field. 2000 MSC: 17B99, 08A72

We study mirror symmetry of families elliptic K3 surfaces with fibers type $E_6,~E_7$ and $E_8$. consider a moduli space $\mathsf{T}$ the enhanced choice differential forms. show that coordinates on are given by ring quasi modular forms in two variables, groups adapted to fiber type. furthermore introduce an algebraic group $\mathsf{G}$ which acts from right construct its Lie algebra $\mathrm{L...

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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...

Let L be a free Lie algebra over a field k, I a non-trivial proper ideal of L, n > 1 an integer. The multiplicator H2(L/I , k) of L/I is not finitely generated, and so in particular, L/I is not finitely presented, even when L/I is finite dimensional.

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...