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. …”
Get full text

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. …”
Get full text

Stability of simultaneously triangularizable switched systems on hybrid domains by Geoffrey Eisenbarth, John M. Davis, Ian Gravagne

“…In particular, we extend the Lie algebraic results in [15] to switched systems with hybrid non-uniform discrete and continuous domains, a direct unifying generalization of switched systems on R and Z, and extend the results in [8, 22] to a larger class of switched systems, namely those whose subsystem matrices are simultaneously triangularizable. …”
Get full text

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.…”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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.…”
Get full text

Generalized parallelizable spaces from exceptional field theory by Pascal du Bosque, Falk Hassler, Dieter Lüst

“…They admit a generalized frame field over the coset space M =G/H which reproduces the Lie algebra g of G under the generalized Lie derivative. …”
Get full text

Local charges in involution and hierarchies in integrable sigma-models by S. Lacroix, M. Magro, B. Vicedo

“…In this general setting, and when the Lie algebra g $$ \mathfrak{g} $$ underlying the r/s-system is of classical type, we construct an infinite algebra of local conserved charges in involution, extending the approach of Evans, Hassan, MacKay and Mountain developed for the principal chiral model and symmetric space σ-model. …”
Get full text

An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras by Adamović, Dražen, Kac, Victor G, Möseneder Frajria, Pierluigi, Papi, Paolo, Perše, Ozren

“…In the case when g is a Lie algebra, we prove a complete reducibility result for Vk(g)-modules at an arbitrary collapsing level. …”
Get full text

New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories by Kannan, Arun S.

“…Each exceptional Lie superalgebra we construct is realized as the image of an exceptional Lie algebra equipped with a nilpotent derivation of order at most p under the semisimplification functor from Repαp to Verp.…”
Get full text

Aggressive formation tracking for multiple quadrotors without velocity measurements over directed topologies by Lin, Jie, Miao, Zhiqiang, Wang, Yaonan, Hu, Guoqiang, Fierro, Rafael

“…Furthermore, an auxiliary system based on Lie algebra is proposed to eliminate the unreliable angular velocity feedback caused by disturbances and bias perturbations. …”
Get full text

Accelerated Newton-Raphson GRAPE methods for optimal control by David L. Goodwin, Mads Sloth Vinding

“…This method, an improvement to the state-of-the-art Newton-Raphson gradient ascent pulse engineering (GRAPE) method, is derived with respect to two exact time-propagator derivative calculation techniques, auxiliary matrix and efficient spin control using analytical Lie algebraic derivatives (ESCALADE) methods. We observed that compared to the best current implementation of the Newton-Raphson GRAPE method, for an ensemble of two-level systems, with realistic conditions, our auxiliary matrix and ESCALADE Hessians can be 4–200 and 70–600 times faster, respectively. …”
Get full text

Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions by Derek K. Wise

“…I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1) and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'.…”
Get full text

Relative Critical Points by Debra Lewis

“…Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures – symplectic, Poisson, or variational – generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. …”
Get full text

A Manipulator Pose Planning Algorithm Based on Matrix Information Geometry by Xiaomin Duan, Anqi Mu, Hao Guo, Xinyu Zhao

“…As the linear operation of the orthogonal matrix corresponding to the manipulator pose is not closed, the manipulator pose at each detected point was calculated using the straightness of the Lie algebra of the special orthogonal group. The matrix information geometry algorithm enabled not only the manipulator to accelerate and decelerate uniformly along the detection trajectory, but also the angular acceleration of the end effector to accelerate uniformly at first, then keep a uniform velocity, and finally decelerate uniformly. …”
Get full text