Generators are found for the field of invariants of coadjoint representations for the Lie algebras that are factors of a unitriangular Lie algebra by some regular ideal.

Abstract. This paper obtains all solvable 3-Lie algebras with the m-dimensional filiform 3-Lie algebra N (m ≥ 5) as a maximal hypo-nilpotent ideal, and proves that the m-dimensional filiform 3-Lie algebra N can’t be as the nilradical of solvable non-nilpotent 3-Lie algebras. By means of one dimensional extension of Lie algebras to the 3-Lie algebras, we get some classes of solvable Lie algebras...

We study simply connected Lie groups $G$ for which the hull-kernel topology of primitive ideal space $\text{Prim}(G)$ group $C^*$-algebra $C^*(G)$ is $T_1$, that is, finite subsets are closed. Thus, we prove AF-embeddable. To this end, show if solvable and its action on centre $[G, G]$ has at least one imaginary weight, then no nonempty quasi-compact open subsets. in addition locally compact wi...

The commutator of Lie algebra is extended to a product of fuzzy Lie subspaces over fuzzy field. An action of fuzzy field is introduced as an extension of scalar multiplication in Lie algebra. The notion of derived series and descending central series of fuzzy Lie ∼ideal over fuzzy field and the concepts of ∼nilpotent and ∼solvable fuzzy Lie ∼ideals over fuzzy field are studied. Mathematics Subj...

Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M . In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U) ⊂ Z, (ii) d(U) ⊂ U and d(U) = 0, (iii) d(U) ⊂ U , d(U) ⊂ Z.

Theorem ([11, Theorem 2, page 282]). Let R be a prime ring, L a noncommutative Lie ideal of R and d 6= 0 a derivation of R. If [d(x), x] ∈ Z(R), for all x ∈ L, then either R is commutative, or char(R) = 2 and R satisfies s4, the standard identity in 4 variables. Here we will examine what happens in case [d(x), x]n ∈ Z(R), for any x ∈ L, a noncommutative Lie ideal of R and n ≥ 1 a fixed integer....

We prove that every finitely generated Lie algebra containing a nilpotent ideal of class c and finite codimension n has Gelfand-Kirillov dimension at most cn. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.

We prove that the only proper right ideal of the universal enveloping algebra of a finite–dimensional central simple Lie triple system over a field of characteristic zero is its augmentation ideal.