Results 1 to 10 of about 852 (252)
On solvable Lie groups of negative Ricci curvature [PDF]
Mathematische Zeitschrift, 2015 We consider the question of whether a given solvable Lie group admits a left-invariant metric of strictly negative Ricci curvature. We give necessary and sufficient conditions of the existence of such a metric for the Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform, and discuss some open questions.
Yuri Nikolayevsky +2 more
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On Surjectivity of the Power Maps of Solvable Lie Groups
Journal of Algebra, 2002 Let \(G\) be a connected solvable Lie group. The author finds conditions under which the power map \(P_n: G\to G\), \(P_ng=g^n\), is surjective. The most detailed results are obtained for the case where \(G\) is a semi-direct product of a compact torus and a simply connected solvable exponential group. If \(G\) is simply connected, the surjectivity of \
exaly +2 more sources
Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent [PDF]
International Journal of Group Theory, 2020 The main result of our consideration is the proof of the centrally nilpotency of class two property for connected topological proper loops $L$ of dimension $\le 3$ which have an at most six-dimensional solvable indecomposable Lie group as their ...
Agota Figula, Ameer Al-Abayechi
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Classification of left invariant metrics on 4-dimensional solvable Lie groups [PDF]
Theoretical and Applied Mechanics, 2020 In this paper the complete classification of left invariant metrics of arbitrary signature on solvable Lie groups is given. By identifying the Lie algebra with the algebra of left invariant vector fields on the corresponding Lie group 𝐺, the ...
Šukilović Tijana
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On LCK solvmanifolds with a property of Vaisman solvmanifolds
Complex Manifolds, 2022 The purpose in this paper is to determine a locally conformal Kähler solvmanifold such that the nilradical of the solvable Lie group is constructed by a Heisenberg Lie group.
Sawai Hiroshi
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Lie algebra classification for the Chazy equation and further topics related with this algebra.
Revista Politécnica, 2021 It is known that the classification of the Lie algebras is a classical problem. Due to Levi’s Theorem the question can be reduced to the classification of semi-simple and solvable Lie algebras.
Yeisson Alexis Acevedo-Agudelo +3 more
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On the Method of Differential Invariants for Solving Higher Order Ordinary Differential Equations
Axioms, 2022 There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case of an nth-order ODE that admits an r-parameter Lie group (3≤r≤n), there is a powerful method of Lie symmetry analysis by which the ODE is
Winter Sinkala, Molahlehi Charles Kakuli
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Pseudo-Riemannian Lie groups admitting left-invariant conformal vector fields
Comptes Rendus. Mathématique, 2020 Let $G$ be a Lorentzian Lie group or a pseudo-Riemannian Lie group of type $(n-2,2)$. If $G$ admits a non-Killing left-invariant conformal vector field, then $G$ is solvable.
Zhang, Hui, Chen, Zhiqi
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ON NILALGEBRAS OVER INFINITE FIELD WITH SOLVABLE ASSOCIATED GROUP
Наука и техника, 2006 It is proved that if an associated group A* of a nilalgebra A over an infinite field is solvable of class n then algebra A is solvable of the same class n as the Lie algebra.
M. B. Smirnov
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Applications of Solvable Lie Algebras to a Class of Third Order Equations
Mathematics, 2022 A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore,
María S. Bruzón +3 more
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