The subject of left-invariant Ricci soliton metrics on nilpotent Lie groups has enjoyed quite a bit of attention in the past several years. These metrics are intimately related to left-invariant Einstein metrics on non-unimodular solvable Lie groups. In fact, a classification of one is equivalent to a classification of the other. In this note, we focus our attention on nilpotent Lie groups and ...

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

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.

To each complex semisimple Lie algebra $$ \mathfrak{g} and regular element a ∈ reg, one associates Mishchenko–Fomenko subalgebra \mathcal{F} ⊆ ℂ[ ]. This amounts to completely integrable system on the Poisson variety , as such has bifurcation diagram Σa Spec( a). We prove that codimension in a) if reg is not nilpotent, it or two nilpotent. In nilpotent case, we show of possible codimensions be ...

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...

In this paper we consider under-actuated, drift-free, invariant systems on matrix Lie groups and show how motion control results for nilpotent systems can be extended to invariant systems on non-nilpotent Lie groups by applying the method of nilpotentization. An algorithm for computing nilpotent approximations for invariant systems on Lie groups is presented. These approximations are used to co...

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small ...

* Correspondence: jinyinlai@lyu. edu.cn School of Science, Linyi University, Linyi 276005, Shandong, P.R. China Full list of author information is available at the end of the article Abstract In this article, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of seventh-degree systems are investigated. With the help of computer algebra system MATHEMATIC...