A simple approach to solve the kinematics and dynamics of the 4-UPS/PS (3R1T) parallel manipulator by Jaime Gallardo-Alvarado, Mario A. García-Murillo, Md Nazrul Islam, Mohammad H. Abedinnasab

“…To this end, the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) is systematically applied to the velocity and reduced acceleration state in screw form of the moving platform cancelling the passive joint rates of the parallel manipulator. …”
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Discrete Minimal Surface Algebras by Joakim Arnlind, Jens Hoppe

“…After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself). …”
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Non-invertible symmetries and higher representation theory II by Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson

“…As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $\mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. …”
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SU(2) symmetry of coherent photons and application to Poincaré rotator by Shinichi Saito

“…Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. …”
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Quantum algorithms for generator coordinate methods by Muqing Zheng, Bo Peng, Nathan Wiebe, Ang Li, Xiu Yang, Karol Kowalski

“…The GCM formalism defined by exponential operators with exponents defined through generators of the fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of probing large subspaces using low-depth quantum circuits. …”
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A classification of real and complex nilpotent orbits of reductive groups in terms of complex even nilpotent orbits by Speh, Peter (Peter Daniel)

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Pure gravities via color-kinematics duality for fundamental matter by Ochirov, A, Johansson, H

“…We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.…”

On the weak N-dependence of SO(N) and SU(N) gauge theories in 2 + 1 dimensions by Athenodorou, A, Lau, R, Teper, M

“…We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N) and SU(N') theories and the equivalence of SO(∞) and SU(∞). …”

Interactions of strings on a T-fold by Yuji Satoh, Yuji Sugawara

“…Our results rely only on general properties of the asymmetric orbifold by the T-duality twist and of the Lie algebra lattice from the symmetry enhancement, and thus may be extended qualitatively to more general T-folds.…”
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Characterizing barren plateaus in quantum ansätze with the adjoint representation by Enrico Fontana, Dylan Herman, Shouvanik Chakrabarti, Niraj Kumar, Romina Yalovetzky, Jamie Heredge, Shree Hari Sureshbabu, Marco Pistoia

“…Using tools from the representation theory of compact Lie groups, we formulate a theory of barren plateaus for parameterized quantum circuits whose observables lie in their dynamical Lie algebra, covering a large variety of commonly used ansätze such as the Hamiltonian Variational Ansatz, Quantum Alternating Operator Ansatz, and many equivariant quantum neural networks. …”
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New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form by Gangwei Wang, Li Li, Qi Wang, Juan Geng

“…First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. …”
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Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality by Dieter Lüst, David Osten

“…We also comment on generalisations of results and techniques known from abelian T -duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T -duality and an application to the investigation of Yang-Baxter deformations. …”
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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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Invariant-based inverse engineering for fast nonadiabatic geometric quantum computation by Wei Li

“…In this paper, based on first given Lewis–Riesenfeld invariant depicted by a unit vector in parameter space, we inverse engineering the time-dependent Hamiltonian of a system with su(2) Lie algebraic structure. The introduced method is then applied to investigate nonadiabatic Abelian geometric quantum computation. …”
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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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Design of a new Robot Operating System-MATLAB-based autonomous robot system and trajectory tracking experiment by Zhenning Yu, Fengxiang Ge, Seng Fat Wong

“…Firstly, the surface robot model is in Lie algebra S O ( 3 ) format, which keeps the potential of cooperation control between space vehicles. …”
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Yang-Baxter deformations of the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) WZW model and non-Abelian T-duality by Ali Eghbali, Tayebe Parvizi, Adel Rezaei-Aghdam

“…Abstract By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie group in twelve inequivalent families. …”
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A quadratic time-dependent quantum harmonic oscillator by F. E. Onah, E. García Herrera, J. A. Ruelas-Galván, G. Juárez Rangel, E. Real Norzagaray, B. M. Rodríguez-Lara

“…Abstract We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set—mass, frequency, driving strength, and parametric pumping—is time-dependent. …”
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Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking by Jerzy Lukierski, Stjepan Meljanac, Salvatore Mignemi, Anna Pachoł

“…In such models, with algebraic basis spanned by oˆ(D,1) Lie algebra generators, we relate the vacuum expectation values (VEV) of the spontaneously broken generators with the Abelian set of ten (Snyder, D=4) or fifteen (Yang, D=5) antisymmetric tensorial generalized coordinates, which are also used as zero order input for obtaining the perturbative solutions of quantum extended Snyder and Yang models. …”
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Lie symmetry analysis for generalized short pulse equation by Zhao Weidong, Munir Muhammad Mobeen, Bashir Hajra, Ahmad Daud, Athar Muhammad

“…Then we will construct the optimal system for the Lie algebra and invariant solutions (called similarity solutions) from Lie subalgebras of generalized SPE.…”
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