Spatially isotropic homogeneous spacetimes by José Figueroa-O’Farrill, Stefan Prohazka

“…We determine the possible limits between the spacetimes and interpret them in terms of contractions of the corresponding transitive Lie algebras. We investigate geometrical properties of the spacetimes such as whether they are reductive or symmetric as well as the existence of invariant structures (riemannian, lorentzian, galilean, carrollian, aristotelian) and, when appropriate, discuss the torsion and curvature of the canonical invariant connection as a means of characterising the different spacetimes.…”
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A CHARACTERIZATION OF DERIVATIONS AND AUTOMORPHISMS ON SOME SIMPLE ALGEBRAS by Farhodjon Arzikulov, Furqatjon Urinboyev, Shahlo Ergasheva

“…In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. …”
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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. …”
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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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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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A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra by Ching Hung Lam, Masahiko Miyamoto

“…Höhn, which relates the weight one Lie algebras of holomorphic VOAs of central charge $24$ to certain codewords associated with the glue codes of Niemeier lattices.…”
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WKB analysis of the linear problem for modified affine Toda field equations by Katsushi Ito, Mingshuo Zhu

“…We explicitly perform this procedure for classical affine Lie algebras with lower ranks. In particular, we study the WKB solutions of the D r 1 $$ {D}_r^{(1)} $$ - and D r + 1 2 $$ {D}_{r+1}^{(2)} $$ -type linear problems, which correspond to the higher-order ODEs with the pseudo-differential operator. …”
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Global tensor‐matter transitions in F‐theory by Dierigl, M, Oehlmann, P, Ruehle, F

“…The six‐dimensional supergravity anomaly constraints are strong enough to completely fix the possible non‐Abelian representations and to restrict the Abelian charges in the hypermultiplet sector affected by the transition, as we demonstrate for all Lie algebras and their representations. Furthermore, we present several examples of such transitions in torically resolved fibrations. …”

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. …”
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Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass by Sara Cruz y Cruz, Oscar Rosas-Ortiz

“…The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian.…”
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Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix by Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites

“…Interesting phenomena in characteristic 2: (1) all simple Lie superalgebras with Cartan matrix are obtained from simple Lie algebras with Cartan matrix by declaring several (any) of its Chevalley generators odd; (2) there exist simple Lie superalgebras whose even parts are solvable. …”
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Duality defects in E 8 by Ivan M. Burbano, Justin Kulp, Jonas Neuser

“…Kac’s theorem for finite automorphisms of Lie algebras and contemporary results on holomorphic VOAs play a role. …”
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A Unified Model of Phantom Energy and Dark Matter by Douglas Singleton, Max Chaves

“…Here we show that theories based on graded Lie algebras naturally have such a negative kinetic energy and thus give a model for phantom energy in a less ad hoc manner. …”
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Classification of second class filiform leibniz algebras in dimension nine by Deraman, Fatanah

“…The third class, TLbn arises from naturally graded filiform Lie algebras. In particular, the study is focused on the classification prob- lem of second class filiform Leibniz algebras, SLbn. …”
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Higher-n triangular dilatonic black holes by Anton Zadora, Dmitri V. Gal'tsov, Chiang-Mei Chen

“…The solutions are derived via the Toda chains for B2 and G2 Lie algebras. They are found in the closed form in general D space–time dimensions. …”
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Characterization of variational quantum algorithms using free fermions by Gabriel Matos, Chris N. Self, Zlatko Papić, Konstantinos Meichanetzidis, Henrik Dreyer

“…By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice – with and without decoupled angles – is able to prepare all fermionic Gaussian states respecting the symmetries of the circuit. …”
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Surveying the quantum group symmetries of integrable open spin chains by Rafael I. Nepomechie, Ana L. Retore

“…Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n(2), A2n−1(2), Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. …”
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Exceptional moduli spaces for exceptional N $$ \mathcal{N} $$ = 3 theories by Justin Kaidi, Mario Martone, Gabi Zafrir

“…As in the case of Lie algebras, the space of CCRGs consists of several infinite families, together with some exceptionals. …”
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Twisted elliptic genera by Kimyeong Lee, Kaiwen Sun, Xin Wang

“…Such objects can arise when the 6d gauge algebra allows outer automorphism, thus are classified by twisted affine Lie algebras. We study several fascinating aspects of the twisted elliptic genera including 2d localization, twisted elliptic blowup equations, Higgsing and spectral flow symmetry. …”
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Finite dimensional Hopf actions on algebraic quantizations by Etingof, Pavel I, Walton, Chelsea

“…This includes universal enveloping algebras of finite dimensional Lie algebras, spherical symplectic reflection algebras, quantum Hamiltonian reductions of Weyl algebras (in particular, quantized quiver varieties), finite W-algebras and their central reductions, quantum polynomial algebras, twisted homogeneous coordinate rings of abelian varieties, and Sklyanin algebras. …”
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