Harmonic Oscillator Coherent States from the Standpoint of Orbit Theory by Alexander Shapovalov, Alexander Breev

“…We have shown that analogs of coherent states constructed by the noncommutative integration can be expressed in terms of the solution to a system of differential equations on the Lie group of the oscillatory Lie algebra. The solutions constructed are directly related to irreducible representation of the Lie algebra on the Hilbert space functions on the Lagrangian submanifold to the orbit of the coadjoint representation.…”
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Symmetries of quaternionic Kähler manifolds with S1‐symmetry by V. Cortés, A. Saha, D. Thung

“…More specifically, we study the metrics obtained by the one‐loop deformation of the c‐map construction, proving that the Lie algebra of infinitesimal automorphisms of the initial projective special Kähler manifold gives rise to a Lie algebra of Killing fields of the corresponding one‐loop deformed c‐map space. …”
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Periodic solutions and symmetry reductions of a generalized Chaffee–Infante equation by I. Humbu, B. Muatjetjeja, T.G. Motsumi, A.R. Adem

“…It will be shown that a generalized Chaffee–Infante equation admits four principal Lie algebra. It will be further shown that the principal Lie algebra admits only one possible extension. …”
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces by Oksana Ye. Hentosh

“…The existence problem of a Hamiltonian representation for the coupled Lax-type hierarchy on a dual space to the central extension of the shift operator Lie algebra is solved also.…”
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Correlated dynamics of immune network and sl(3, R) symmetry algebra by Dutta Ruma, Stan Aurel

“…We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. …”
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Yang–Baxter maps, discrete integrable equations and quantum groups by Vladimir V. Bazhanov, Sergey M. Sergeev

“…For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang–Baxter equation. …”
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Supersymmetric BKP systems and their symmetries by Chuanzhong Li, Jingsong He

“…These additional flows constitute a B type SW1+∞ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy. …”
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Varieties of a class of elementary subalgebras by Yang Pan, Yanyong Hong

“…Let $ G $ be a connected standard simple algebraic group of type $ C $ or $ D $ over an algebraically closed field $ \Bbbk $ of positive characteristic $ p > 0 $, and $ \mathfrak{g}: = \mathrm{Lie}(G) $ be the Lie algebra of $ G $. Motivated by the variety of $ \mathbb{E}(r, \mathfrak{g}) $ of $ r $-dimensional elementary subalgebras of a restricted Lie algebra $ \mathfrak{g} $, in this paper we characterize the irreducible components of $ \mathbb{E}(\mathrm{rk}_{p}(\mathfrak{g})-1, \mathfrak{g}) $ where the $ p $-rank $ \mathrm{rk}_{p}(\mathfrak{g}) $ is defined to be the maximal dimension of an elementary subalgebra of $ \mathfrak{g} $.…”
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Representations having vectors fixed by a Levi subgroup associated to a real form by Smilga, I

“…For any semisimple real Lie algebra gR, we classify the representations of gR that have at least one nonzero vector on which the centralizer of a Cartan subspace, also known as the centralizer of a maximal split torus, acts trivially. …”

Crystals and affine Hecke algebras of type D by Kashiwara, M, Miemietz, V

“…The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra $g$ where $g$ is $gl_\infty$ or the affine Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to the upper global bases. …”

A SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLE by Satoshi Ohya

“…We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. …”
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A Stochastic Poisson Structure by Rémi Léandre

“…We define a Poisson structure on the Nualart-Pardoux test algebra associated to the path space of a finite dimensional Lie algebra.…”
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Quantum Integrable Model of an Arrangement of Hyperplanes by Alexander Varchenko

“…The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of affine hyperplanes. …”
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L∞ algebras and field theory by Hohm, Olaf, Zwiebach, Barton

“…Theories where the gauge structure is a strict Lie algebra often require the full L∞algebra for the interacting theory. …”
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Normal form of particle motion under the influence of an ac dipole by R. Tomás

“…The particle motion to first order in the nonlinearities is derived using Lie algebra techniques. The dependence of the Hamiltonian terms on the longitudinal coordinate is studied showing that they vary differently depending on the ac dipole parameters. …”
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Highest weight modules at the critical level and noncommutative Springer resolution by Bezrukavnikov, Roman, Lin, Qian

“…Let gˇ be the Langlands dual Lie algebra and let [˄ over g] be the corresponding affine Lie algebra, i.e. [˄ over g] is a central extension of gˇ ⊗ C((t)). …”
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FONDASI MATEMATIS TEORI TERA: KAJIAN TENTANG UNTINGAN SERAT, KONEKSI DAN KELENGKUNGAN by , LALU MUHAMMAD ABDI ZAMAKHSYARI, , Dr.rer.nat. Muhammad Farchani Rosyid

“…After that, connection is interpreted as Lie algebra-valued 1-form on principal fiber bundle to get the local picture of connection in base manifold. …”

Intrinsic stratifications of analytic varieties by François Treves

“…By associating a Lie algebra of analytic vector elds to every point of an analytic variety and using the associated Nagano foliation, this work presents a coordinate-free stratication of analytic sets.…”
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Beilinson–Drinfeld Schubert varieties and global Demazure modules by Ilya Dumanski, Evgeny Feigin, Michael Finkelberg

“…The answer is given in terms of global Demazure modules over the current Lie algebra.…”
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On the Quantum Deformations of Associative Sato Grassmannian Algebras and the Related Matrix Problems by Alexander A. Balinsky, Victor A. Bovdi, Anatolij K. Prykarpatski

“…We analyze the Lie algebraic structures related to the quantum deformation of the Sato Grassmannian, reducing the problem to studying co-adjoint orbits of the affine Lie subalgebra of the specially constructed loop diffeomorphism group of tori. …”
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