On the kinematic algebra for BCJ numerators beyond the MHV sector by Gang Chen, Henrik Johansson, Fei Teng, Tianheng Wang

“…Abstract The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. …”
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Emergence of spacetime from the algebra of total modular Hamiltonians by Daniel Kabat, Gilad Lifschytz

“…On fields with gauge redundancies the total modular Hamiltonian acts as a bulk Lie derivative together with a compensating bulk gauge (or diffeomorphism) transformation to restore the original gauge. We consider the Lie algebra generated by the total modular Hamiltonians of all spherical CFT subregions and define weakly-maximal Lie subalgebras as proper subalgebras containing a maximal set of total modular Hamiltonians. …”
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Neural correlates of hallucinations in bipolar disorder by Maila de C. Neves, Dante G. Duarte, Maicon R. Albuquerque, Rodrigo Nicolato, Fernando S. Neves, Fábio L. de Souza-Duran, Geraldo Busatto, Humberto Corrêa

“…Preprocessing was performed using the Diffeomorphic Anatomical Registration through Exponentiated Lie Algebra (DARTEL) algorithm for VBM in SPM8. Images were processed using optimized VBM. …”
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SO(N) gauge theories in 2+1 dimensions: Glueball spectra and confinement by Lau, R, Teper, M

“…We also compare the glueball spectra of those pairs of SO(N) and SU(N') theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)XSU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. …”

Geometric invariant theory for graded unipotent groups and applications by Berczi, G, Doran, B, Hawes, T, Kirwan, FC

“…Let U be a graded unipotent group over the complex numbers, in the sense that it has an extension U by the multiplicative group such that the action of the multiplicative group by conjugation on the Lie algebra of U has all its weights strictly positive. …”

Hyperkähler and quaternionic Kähler geometry by Swann, A

“…</p> <p>Nilpotent orbits in a complex semi-simple Lie algebra, with the hyperKähler metrics defined by Kronheimer, are shown to give rise to quaternionic Kähler metrics and various examples of these metrics are identified. …”

The Structure of GUT Breaking by Orbifolding by Hebecker, A, March-Russell, J

“…This depends upon the existence of appropriate inner and outer automorphisms of the Lie algebra, and we show that a reduction of the rank of the GUT group is possible. …”

Can shallow quantum circuits scramble local noise into global white noise? by Foldager, J, Koczor, B

“…Lastly, we identify techniques that may decrease both metrics, such as increasing the dimensionality of the dynamical Lie algebra by gate insertions or randomised compiling.…”

Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases by Zhifei Zhang, Guowei Liu, Beiping Hou, Jinrong Li

“…A geometric proportional–integral–derivative (PID) controller is proposed with all the input commands defined in the dual space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="fraktur">so</mi><mo>*</mo></msup><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of a Lie algebra for left-invariant systems evolving on a Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Trajectory tracking control strategy of the gantry welding robot under the influence of uncertain factors by Hongwei Sun, Haonan Wang, Yicun Xu, Jiong Yang, Yujie Ji, Lei Cheng, Chao Liu, Benshun Zhang

“…Screw theory and Lie group lie algebra are used to solve the problem of high algorithm complexity of controllers in multi-degree-of-freedom robot systems due to Newton-Euler dynamics modeling. …”
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A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation by Naseem Abbas, Akhtar Hussain, Muhammad Bilal Riaz, Tarek F. Ibrahim, F.M. Osman Birkea, R. Abdelrahman Tahir

“…The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). …”
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Integrated Geometric Optimal Control of Spacecraft Attitude and Orbit Based on <italic>SE</italic>(3) by Zhongzhong Zheng, Wei Shang, Jia Ai, Yuhan Zou, Zhou Liu

“…Then, based on differential geometric theories, such as the variational principle, the left-invariant principle of Lie group, and the topology of Lie algebraic space, MPCP is applied to <inline-formula> <tex-math notation="LaTeX">$SE(3)$ </tex-math></inline-formula>. …”
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Big Bang and Topology by Torsten Asselmeyer-Maluga, Jerzy Król, Alissa Wilms

“…Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>q</mi></msub><mrow><mo>(</mo><mi>s</mi><msub><mi>l</mi><mn>2</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">C</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <i>q</i> is the fourth root of unity.…”
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Generalised U-dual solutions in supergravity by Chris D. A. Blair, Sofia Zhidkova

“…These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. …”
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Diagnosing Barren Plateaus with Tools from Quantum Optimal Control by Martin Larocca, Piotr Czarnik, Kunal Sharma, Gopikrishnan Muraleedharan, Patrick J. Coles, M. Cerezo

“…Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra $\mathfrak{g}$ obtained from the generators of the ansatz. …”
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Large Scale Emerging Properties from Non Hamiltonian Complex Systems by Marco Bianucci

“…Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. …”
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A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry by Chris D. A. Blair, Domingo Gallegos, Natale Zinnato

“…We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.…”
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Qudit Entanglers Using Quantum Optimal Control by Sivaprasad Omanakuttan, Anupam Mitra, Eric J. Meier, Michael J. Martin, Ivan H. Deutsch

“…We take advantage of both continuous, Lie algebraic control and digital, Lie group control. …”
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Cosmology as a CFT1 by Jibril Ben Achour, Etera R. Livine

“…On the one hand, we identify the corresponding conformal Noether charges, as combinations of the Hamiltonian scalar constraint, the extrinsic curvature and the 3D volume, which form a closed 𝔰𝔩 (2, ℝ) Lie algebra. On the other hand, this approach allows to write FLRW cosmology in terms of a AdS2 phase space and a Schwarzian action. …”
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Pseudo-hermitian random matrix models: General formalism by Joshua Feinberg, Roman Riser

“…As a concrete example, which is essentially an ensemble of elements of the non-compact unitary Lie algebra, we choose a particularly simple set of metrics, and compute the resulting resolvent and density of eigenvalues in closed form. …”
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