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Representations of Solvable Lie Groups
2020The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations ...
Didier Arnal, Bradley Currey
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Analysis of a Distinguished Laplacian on Solvable Lie Groups
Mathematische Nachrichten, 1993AbstractWe study a class of kernels associated to functions of a distinguished Laplacian on the solvable group AN occurring in the Iwasawa decomposition G = ANK of a noncompact semisimple Lie group G. We determine the maximal ideal space of a commutative subalgebra of L1, which contains the algebra generated by the heat kernel, and we prove that the ...
MAUCERI, GIANCARLO, GIULINI, SAVERIO
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On the Surjectivity of the Exponential Function of Solvable Lie Groups
Mathematische Nachrichten, 1998AbstractFor a solvable Lie group G the surjectivity of the exponential function expG is equivalent to the connectedness of the near‐Cartan subgroups and to the connectedness of the centralizers in a Cartan subgroup of all nilpotent elements in its Lie algebra g.
Michael Wüstner
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A poisson formula for solvable Lie groups
Journal d'Analyse Mathématique, 1996Given 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 ...
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On the Symmetries of Five-Dimensional Solvable Lie Groups
Journal of Lie Theory, 2020Summary: 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, 2019A 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, 1999The 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
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A Beurling Theorem for Exponential Solvable Lie Groups
Journal of Lie Theory, 2015For 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, 2021The 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, 1996A 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 +1 more
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