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The relation between the symplectic group Sp(4,R) and its Lie algebra: Applications to polymer quantum mechanics [PDF]
Physical Review D, 2021 In this paper, we show the relation between $sp(4,\mathbb{R})$, the Lie algebra of the symplectic group, and the elements of $Sp(4,\mathbb{R})$. We use this result to obtain some special cases of symplectic matrices relevant to the study of squeezed ...
G. Chac'on-Acosta, A. Garc'ia-Chung
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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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SCENE CLASSIFICATION BASED ON THE INTRINSIC MEAN OF LIE GROUP [PDF]
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2020 Remote Sensing scene classification aims to identify semantic objects with similar characteristics from high resolution images. Even though existing methods have achieved satisfactory performance, the features used for classification modeling are still ...
C. Xu, G. Zhu, K. Yang
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Cohomology of nonabelian embedding tensors on Hom-Lie algebras
AIMS Mathematics, 2023 In this paper, we generalize known results of nonabelian embedding tensor to the Hom setting. We introduce the concept of Hom-Leibniz-Lie algebra, which is the basic algebraic structure of nonabelian embedded tensors on Hom-Lie algebras and can also be ...
Wen Teng , Jiulin Jin, Yu Zhang
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Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3 nilpotent Lie group [PDF]
Journal of Physics A: Mathematical and Theoretical, 2018 The paper presents a new method of geometric solution of a Schrödinger equation by constructing an equivalent first-order partial differential equation with a bigger number of variables.
Fadhel Almalki, V. Kisil
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Lie Group Equivariant Convolutional Neural Network Based on Laplace Distribution
Remote Sensing, 2023 Traditional convolutional neural networks (CNNs) lack equivariance for transformations such as rotation and scaling. Consequently, they typically exhibit weak robustness when an input image undergoes generic transformations.
Dengfeng Liao, Guangzhong Liu
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Screw and Lie group theory in multibody dynamics [PDF]
Multibody system dynamics, 2017 Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms.
A. Müller
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Entropy, 2023 The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the
J. A. López-Saldívar +3 more
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Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
Journal of High Energy Physics, 2021 We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models.
Pasquale Calabrese +2 more
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The universal representation kernel of a Lie group [PDF]
Proceedings of the American Mathematical Society, 1960 Let G be a connected real Lie group. The universal representation kernel, Ko, oi G is defined as the intersection of all kernels of continuous finite dimensional representations of G. Evidently, Ko is a closed normal subgroup of G, and it is known from a theorem due to Goto (cf.
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