On the geometry of Riemannian manifolds with a Lie structure at infinity by Bernd Ammann, Robert Lauter, Victor Nistor

“…We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.…”
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Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution by H. Panahi, M. Baradaran

“…We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. …”
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Algebro-Geometric Solutions for a Discrete Integrable Equation by Mengshuang Tao, Huanhe Dong

“…With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. …”
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The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures by Juhui Zhang, Yuqin Yao

“…Furthermore, based on the semidirect sums of matrix Lie algebras consisting of 3×3 block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.…”
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Bi-Integrable Couplings of a New Soliton Hierarchy Associated with SO(4) by Yan Cao, Liangyun Chen, Baiying He

“…Based on the six-dimensional real special orthogonal Lie algebra SO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. …”
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Algebraic Structures Based on a Classifying Space of a Compact Lie Group by Dae-Woong Lee

“…We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. …”
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Pseudo-Sasakian manifolds endowed with a contact conformal connection by Vladislav V. Goldberg, Radu Rosca

“…It is proved that such manifolds are space forms M˜(K), K<0, and some remarkable properties of the Lie algebra of infinitesimal transformations of the principal vector field U˜ on M˜ are discussed. …”
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Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem by R. J. Moitsheki, M. D. Mhlongo

“…We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. …”
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Time-Compact Scheme for the One-Dimensional Dirac Equation by Jun-Jie Cao, Xiang-Gui Li, Jing-Liang Qiu, Jing-Jing Zhang

“…Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. …”
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On the space of 2d integrable models by Lukas W. Lindwasser

“…Abstract We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of 2d integrable models. …”
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Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance by Tanki Motsepa, Chaudry Masood Khalique, Motlatsi Molati

“…We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. …”
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Three-dimensional non-relativistic Hietarinta supergravity by Patrick Concha, Evelyn Rodríguez, Sebastián Salgado

“…To incorporate supersymmetry, we apply the Lie algebra expansion method to obtain the non-relativistic formulation of $${\mathcal {N}}=2$$ N = 2 Hietarinta supergravity. …”
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Analysis of Stiffness Characteristic of Five-degree-of-freedom Hammer Riveting Robot based on Spiral Theory by Chunying Jiang, Xiangchen Liu, Changlong Ye, Huan Zhou, Xu Guan

“…In view of the characteristics of the 5-DOF hammer riveting robot， combining Lie group Lie algebra and spiral theory， its kinematics model is established and solved； use the exponential product formula to derive the Jacobian matrix of the robot，and use the stiffness mapping theory to solve the stiffness matrix of the robot； the finite element and Matlab simulation software are used to simulate and verify the end deformation under the general pose and the extreme pose，and the stiffness distribution map of the robot in the task space varying with the change of pose is given；the simulation result is compared with the theoretical calculation value and the error is not more than 10%，which verify the correctness and effectiveness of the established stiffness model and provide important reference for optimization of subsequent work path.…”
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(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves by Chunlei Wang, Yong Zhang, Baoshu Yin, Xiaoen Zhang

“…By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. …”
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A Closed Form of Higher-Order Cayley Transforms and Generalized Rodrigues Vectors Parameterization of Rigid Motion by Daniel Condurache, Mihail Cojocari, Ioan-Adrian Ciureanu

“…The transform is defined by the Lie algebra of three-dimensional vectors into the Lie group of proper orthogonal Euclidean tensors. …”
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Lie symmetries, closed-form solutions, and conservation laws of a constitutive equation modeling stress in elastic materials by Rehana Naz, Willy Hereman

“…The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was investigated by Mason and his collaborators (Magan et al., 2018). The Lie algebra for the model is five-dimensional for the shearing exponent n>0, and it includes translations in time, space, and displacement, as well as time-dependent changes in displacement and a scaling symmetry. …”
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The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics by Yan Gu, Jiao Wang

“…As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. …”
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SUBJECT «NUMBER SYSTEMS» IN TWO-LEVELED FORMAT PREPARATION TEACHERS OF MATHEMATICS by V. I. Igoshin

“…Here we study algebras over a field, division algebra over a field, an alternative algebra with division over the field, Jordan algebra, Lie algebra. Comprehension of bases of the theory of algebras by the master of the «mathematical education» profile will promote more conscious understanding of an axiomatic method, a structure of axiomatic theories in mathematics, development mechanisms of mathematical science; at the same time it will help to develop to complete vision of mathematics as a single science. …”
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A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations by A. Fatima, Muhammad Ayub, F. M. Mahomed

“…We provide a supplementation of the results on the canonical forms for scalar fourth-order ordinary differential equations (ODEs) which admit four-dimensional Lie algebras obtained recently. Together with these new canonical forms, a complete list of scalar fourth-order ODEs that admit four-dimensional Lie algebras is available.…”
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Transformation groups on real plane and their differential invariants by Maryna O. Nesterenko

“…As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.…”
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