Special symplectic Lie groups and hypersymplectic Lie groups [PDF]
manuscripta mathematica, 2010 32 ...
Chengming Bai, Xiang Ni
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Research on the Necessity of Lie Group Strapdown Inertial Integrated Navigation Error Model Based on Euler Angle [PDF]
Sensors, 2022 In response to the lack of specific demonstration and analysis of the research on the necessity of the Lie group strapdown inertial integrated navigation error model based on the Euler angle, two common integrated navigation systems, strapdown inertial ...
Leiyuan Qian +3 more
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Multi-Stage Meta-Learning for Few-Shot with Lie Group Network Constraint [PDF]
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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Lie Group Methods in Blind Signal Processing [PDF]
Sensors, 2020 This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamentals of
Dariusz Mika, Jerzy Jozwik
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Pro-Lie Groups: A Survey with Open Problems
Axioms, 2015 A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete ...
Karl H. Hofmann, Sidney A. Morris
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Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds [PDF]
Nuclear Physics B, 2018 Using the concept of Jacobi–Lie group and Jacobi–Lie bialgebra, we generalize the definition of Poisson–Lie symmetry to Jacobi–Lie symmetry. In this regard, we generalize the concept of Poisson–Lie T-duality to Jacobi–Lie T-duality and present Jacobi–Lie
A. Rezaei-Aghdam, M. Sephid
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Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics [PDF]
Entropy, 2020 In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau’s symplectic model of statistical ...
Frédéric Barbaresco +1 more
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Linearization of Poisson Lie group structures [PDF]
, 2013 We show that for any coboundary Poisson Lie group G, the Poisson structure on G^* is linearizable at the group unit. This strengthens a result of Enriquez-Etingof-Marshall, who had established formal linearizability of G^* for quasi-triangular Poisson ...
A. Alekseev, E. Meinrenken
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Lie group integrators for mechanical systems [PDF]
International Journal of Computational Mathematics, 2021 Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two important classes
E. Celledoni +4 more
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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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