Continuous-time quantum harmonic oscillator state engineering by E García Herrera, F Torres-Leal, B M Rodríguez-Lara

“…We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.…”
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Generalized teleparallel de Sitter geometries by A. A. Coley, A. Landry, R. J. van den Hoogen, D. D. McNutt

“…In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.…”
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THE SOCCER-BALL PROBLEM IN QUANTUM SPACE by KHRYSTYNA P. GNATENKO, VOLODYMYR M. TKACHUK

“…It is shown that this problem can be solved in a deformed space with a minimal length, in a noncommutative phase space, in a space with a Lie-algebraic noncommutativity, in a twist-deformed space-time due to the relation of parameters of corresponding algebras with mass. …”
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Linear entropy and squeezing of the interaction between two quantum system described by su (1, 1) and su(2) Lie group in presence of two external terms by M. Sebawe Abdalla, E. M. Khalil, A. S.-F. Obada, J. Peřina, J. Křepelka

“…A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. …”
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Cohomology of simple modules for sl3(k) in characteristic 3 by A.A. Ibrayeva

“… In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. …”
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Abelian extensions of Lie triple systems with derivations by Xueru Wu, Yao Ma, Liangyun Chen

“…. $ We first construct the third-order cohomology classes by derivations of $ A $ and $ \mathfrak{L}, $ then obtain a Lie algebra $ G_{\theta_A} $ with a representation $ \Phi $ on $ H^3(\mathfrak{L}, A), $ where $ \theta_A $ is given by an abelian extension $ 0\longrightarrow A\longrightarrow {\tilde {\mathfrak{L}}} \xrightarrow{\pi} \mathfrak{L}\longrightarrow 0. $ We study obstruction classes for extensibility of derivations of $ A $ and $ \mathfrak{L} $ to those of $ \tilde{\mathfrak{L}}. $ An application of $ \Phi $ is discussed.…”
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RELATIVE COMPLETE REDUCIBILITY AND NORMALIZED SUBGROUPS by MAIKE GRUCHOT, ALASTAIR LITTERICK, GERHARD RÖHRLE

“…We also derive analogous results for Lie subalgebras of the Lie algebra of $G$, as well as ‘rational’ versions over nonalgebraically closed fields.…”
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The Small Quantum Group as a Quantum Double by Etingof, Pavel I., Gelaki, Shlomo

“…J. 5 (2) (2005) 371–378] to a simple complex Lie algebra g and a primitive root of unity q of order n2 is equivalent to Lusztig’s small quantum group uq(g) (under some conditions on n). …”
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Ghost-Free Superconformal Action for Multiple M2-Branes by Bandres, M, Lipstein, A, Schwarz, J

“…Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. …”

The symplectic and twister geometry of the general isomonodromic deformation problem by Woodhouse, N

“…This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group. © 2001 Elsevier Science B.V.…”

Ghost-free superconformal action for multiple M2-branes by Bandres, M, Lipstein, A, Schwarz, J

“…Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. …”

Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory by Da Bin Jeong, Nak Yong Ko

“…The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). …”
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On representations of quantum groups and Cherednik algebras by Balagović, Martina

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Generalized cosmological constant from gauging Maxwell-conformal algebra by Salih Kibaroğlu, Oktay Cebecioğlu

“…We subsequently find the generalized Einstein field equation together with a coordinate dependent cosmological term and additional contributions. Keywords: Lie algebra, Gauge field theory, Modified theory of gravity, Cosmological constant…”
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Space, Matter and Interactions in a Quantum Early Universe Part I: Kac–Moody and Borcherds Algebras by Piero Truini, Alessio Marrani, Michael Rios, Klee Irwin

“…We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac–Moody Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="bold">e</mi><mn mathvariant="bold">9</mn></msub></semantics></math></inline-formula>. …”
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Affine characters at negative level and elliptic genera of non-critical strings by David Jaramillo Duque, Amir-Kian Kashani-Poor

“…We formulate a general ansatz for these in terms of characters of the affine Lie algebra associated to the 6d gauge group at negative level, and provide ample evidence for the validity of this ansatz for 6d theories obtained via F-theory compactification on elliptically fibered Calabi-Yau manifolds over a Hirzebruch base. …”
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A (1+2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions by Maksym Didovych

“…It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller–Segel system in question were found. …”
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Cosmological Finsler Spacetimes by Manuel Hohmann, Christian Pfeifer, Nicoleta Voicu

“…Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. …”
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Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit–qubit interaction by S. Abdel-Khalek, Hashim M. Alshehri, E. M. Khalil, A.-S. F. Obada

“…Abstract The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit–qubit interaction and dissipation term is considered. …”
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Steps towards generalization of tensionless string theory with contact interactions as Wilson loop of non-Abelian Yang–Mills theory by Pongwit Srisangyingcharoen

“…To reproduce path-ordering along the worldsheet boundary, we introduce Lie algebra-valued fields on the string worldsheet, whose dynamics are determined by the topological BF action. …”
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