Results 201 to 210 of about 649 (235)

On the derived length of Lie solvable group algebras

Publicationes Mathematicae Debrecen, 2006
Summary: Let \(G\) be a nilpotent group with cyclic commutator subgroup of order \(p^n\) and let \(F\) be a field of characteristic \(p\). It is shown here that the Lie derived length of the group algebra \(FG\) is at most \(\lceil\log_2(p^n+1)\rceil\). Furthermore, this bound is achieved if and only if one of the following conditions is satisfied: (i)
openaire   +2 more sources

Exponentiality of Certain Real Solvable Lie Groups

Canadian Mathematical Bulletin, 1998
AbstractIn this article, making use of the second author’s criterion for exponentiality of a connected solvable Lie group, we give a rather simple necessary and sufficient condition for the semidirect product of a torus acting on certain connected solvable Lie groups to be exponential.
Moskowitz, Martin, Wüstner, Michael
openaire   +1 more source

Homogeneous geodesics in solvable Lie groups

Acta Mathematica Hungarica, 2003
Let \((G/H,g)\) be a (connected) homogeneous Riemannian manifold. A homogeneous geodesic through the origin of \(G/H\) is by definition a geodesic which is an orbit of a one-parameter subgroup of \(G\). The second author and \textit{J. Szenthe} [Geom. Dedicata 81, No. 1--3, 209--214 (2000; Zbl 0980.53061); erratum ibid. 84, No.
CALVARUSO, Giovanni, O. KOWALSKI, MARINOSCI, Rosa Anna   +2 more
openaire   +4 more sources

Abelian Groups with Solvable Lie Endomorphism Rings

Russian Mathematics
A description has been obtained of all divisible, primary, as well as separable and algebraically compact torsion-free groups, the Lie endomorphism ring of which is solvable.
openaire   +2 more sources

Lie solvable group algebras and solvable unit group

2007
This note is a short survey of recent results and open problems in the framework of Lie solvable group algebras.
openaire   +2 more sources

Rigidity of group actions on solvable Lie groups

Mathematische Annalen, 2000
In this paper, as in other mathematical studies, a crystallographic group denotes a space group which is a discrete cocompact subgroup of the Euclidean group \(E(d)=\mathbb{R}^d\rtimes O(d)\). Space groups are not only important from the point of view of physics, as symmetry groups of crystals, but mathematically as well, because of interrelations ...
openaire   +2 more sources

Controllability of right-invariant systems on solvable lie groups

Journal of Dynamical and Control Systems, 1997
Following the lines of his paper reviewed above, the author gives various conditions that are necessary or sufficient (sometimes both) for the controllability of invariant affine control systems on Lie groups. The main hypothesis made is the existence of codimension-one subgroups what makes the author's ``hypersurface principle'' work.
openaire   +2 more sources

Local derivations on Solvable Lie algebras

Linear and Multilinear Algebra, 2021
Abror Khudoyberdiyev, Sh A Ayupov
exaly  

On the Cohomology of Lattices in Solvable Lie Groups

The Annals of Mathematics, 1966
openaire   +2 more sources

Homogeneous Geodesics of $4$-dimensional Solvable Lie Groups

International Electronic Journal of Geometry
We study homogeneous geodesics in $4$-dimensional solvable Lie groups $\mathrm{Sol}_0^4$, $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}$ and $\mathrm{Nil}_4$.
openaire   +3 more sources