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Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2023 An important subclass among homogeneous spaces is formed by isotropically-faithful homogeneous spaces, in particular, this subclass contains all homogeneous spaces admitting invariant affine connection.
Mozhey, Natalya Pavlovna
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Advances in the Theory of Compact Groups and Pro-Lie Groups in the Last Quarter Century
Axioms, 2021 This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century.
Karl H. Hofmann, Sidney A. Morris
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Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements
Mathematics, 2020 The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements.
Daniel Condurache, Ioan-Adrian Ciureanu
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Survey on Lie Group Machine Learning
Big Data Mining and Analytics, 2020 Lie group machine learning is recognized as the theoretical basis of brain intelligence, brain learning, higher machine learning, and higher artificial intelligence. Sample sets of Lie group matrices are widely available in practical applications.
Mei Lu, Fanzhang Li
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Geometry of Tangent Poisson–Lie Groups
Mathematics, 2023 Let G be a Poisson–Lie group equipped with a left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on G to the tangent bundle TG of G.
Ibrahim Al-Dayel +2 more
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On the Solution of the Schrödinger Equation with Position-Dependent Mass
Universe, 2020 We have considered the Iwasawa and Gauss decompositions for the Lie group SL(2,R). According to these decompositions, the Casimir operators of the group and the Hamiltonians with position-dependent mass were expressed.
Mehmet Sezgin
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Local Lie groups and local top spaces
Journal of the Egyptian Mathematical Society, 2016 In this paper a generalization of local Lie groups, using the concept of top spaces, is given and some theorems about the relation between this generalization and local Lie groups are provided.
N. Ebrahimi
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Multi-Stage Meta-Learning for Few-Shot with Lie Group Network Constraint
Entropy, 2020 Deep learning has achieved many successes in different fields but can sometimes encounter an overfitting problem when there are insufficient amounts of labeled samples.
Fang Dong, Li Liu, Fanzhang Li
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An example of a non-Borel locally-connected finite-dimensional topological group
Karpatsʹkì Matematičnì Publìkacìï, 2017 According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of ...
I.Ya. Banakh, T.O. Banakh, M.I. Vovk
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Einstein warped product spaces on Lie groups
Cubo, 2022 We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, $M = M_1 \times_{f_1} M_2$ for the cases, $(i)$ $M_1$ is a Lie group $(ii)$ $M_2$ is a Lie group and $(iii ...
Buddhadev Pal +2 more
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