Results 221 to 230 of about 858 (252)

A poisson formula for solvable Lie groups

Journal d'Analyse Mathématique, 1996
Given a probability measure \(\mu\) on a locally compact group \(G\) a bounded Borel function \(h:G \to\mathbb{C}\) is called \(\mu\)-harmonic if it satisfies the \(\mu\)-mean value property, viz. \(h(g)= \int_Gh(gg') \mu(dg')\), \(g\in G\). It is known that certain conditions on \(G\) and \(\mu\) lead to the Poisson representation for such functions ...
openaire   +1 more source

On the Symmetries of Five-Dimensional Solvable Lie Groups

Journal of Lie Theory, 2020
Summary: We consider a five-dimensional solvable Lie group, equipped with a left-invariant Riemannian metric. We obtain a full classification of Killing and affine vector fields as well as Ricci, curvature and matter collineations.
Mostefaoui, Assia, Belarbi, Lakehal
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The Topological Generating Rank of Solvable Lie Groups

Journal of Lie Theory, 2019
A subset \(X\) of a topological group \(G\) is said to be a topological generating set for \(G\) if the smallest closed subgroup containing \(X\) is \(G\) itself, or, equivalently, the group generated by \(X\) is dense in \(G\). Therefore and in this paper, the authors define the topological generating rank \(d(G)\) of a connected Lie group \(G\) as ...
Abels, Herbert, Noskov, Gennady A.
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REPRESENTATIONS OF SOLVABLE LIE GROUPS AND GEOMETRIC QUANTIZATION

Chinese Annals of Mathematics, 1999
The paper under review uses the theory of geometric quantization for solvable Lie groups developed by Kostant-Sourian and Auslander-Kostant to quantize the covering spaces of coadjoint orbits of solvable Lie groups. The main theorem is that for each integral coadjoint orbit \(O\) and each element \(\sigma\) in the fundamental group \(\pi_1(O)\) of \(O\)
Zhao, Qiang, Xiao, Li
openaire   +2 more sources

A Beurling Theorem for Exponential Solvable Lie Groups

Journal of Lie Theory, 2015
For an exponential solvable Lie group \(G\) with non-trivial center, the authors show that a measurable function \(f\) on \(G\) satisfying \[ \int_G\int_{\mathcal W}|f(g)|^2\|K_\xi^{1/2}\pi_\xi(f)\|^2_{HS} e^{2\|g\|\|\xi\|}\,dg\,d ...
Alghamdi, Ahmad M. A., Baklouti, Ali
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A Version of Lie Theorem for Divisible Solvable Groups

Russian Journal of Mathematical Physics, 2021
The well known Lie-Kolchin theorem asserts that a soluble linear group over an algebraically closed field contains a triangularizable subgroup of finite index (see for instance Theorem 5.8 of [\textit{B. A. F. Wehrfritz}, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices.
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HYPERCOMPLEX STRUCTURES ON A CLASS OF SOLVABLE LIE GROUPS

The Quarterly Journal of Mathematics, 1996
A hypercomplex manifold is a triple \((M, J_1, J_2)\) consisting of a \(4n\)-dimensional manifold together with two anticommuting complex structures. This paper concerns the construction of non-compact homogeneous manifolds carrying such a structure; the compact case has been considered by \textit{D. D. Joyce} [J. Differ. Geom.
Barberis, María Laura, Dotti Miatello, Isabel   +1 more
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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)
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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
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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
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