Exact solution of the sp(4) integrable spin chain with generic boundaries by Guang-Liang Li, Junpeng Cao, Panpan Xue, Zhi-Rong Xin, Kun Hao, Wen-Li Yang, Kangjie Shi, Yupeng Wang

“…Abstract The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the sp(4) (or C 2) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. …”
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On the weak N-dependence of SO(N) and SU(N) gauge theories in 2+1 dimensions by Andreas Athenodorou, Richard Lau, Michael Teper

“…We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N) and SU(N′) theories and the equivalence of SO(∞) and SU(∞). …”
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Classical W-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents by Valeri, Daniele, Sole, Alberto De, Kac, Victor

“…We derive explicit formulas for λ-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding integrable generalized Drinfeld–Sokolov hierarchies. …”
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Structure of classical (finite and affine) W-algebras by De Sole, Alberto, Kac, Victor, Valeri, Daniele

“…First, we derive an explicit formula for the Poisson bracket of the classical finite W- Algebra W[superscript fin] (g, f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f . On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W- Algebra W(g, f). …”
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Euler characteristics of Hilbert schemes of points on surfaces with simple singularities by Szendroi, B, Gyenge, A, Nemethi, A

“…The generating series in our conjecture can be seen as a specialized character of the basic representation of the corresponding (extended) affine Lie algebra; we discuss possible representation-theoretic consequences of this fact. …”

A simple approach to solve the kinematics and dynamics of the 4-UPS/PS (3R1T) parallel manipulator by Jaime Gallardo-Alvarado, Mario A. García-Murillo, Md Nazrul Islam, Mohammad H. Abedinnasab

“…To this end, the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) is systematically applied to the velocity and reduced acceleration state in screw form of the moving platform cancelling the passive joint rates of the parallel manipulator. …”
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The PBW Filtration, Demazure Modules and Toroidal Current Algebras by Evgeny Feigin

“…Let L be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra ^g. The m-th space F_m of the PBW filtration on L is a linear span of vectors of the form x_1dots x_lv_0, where l ≤ m, x_i in ^g and v_0 is a highest weight vector of L. …”
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Solution of the classical Yang–Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model by Jon Links

“…Solutions of the classical Yang–Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang–Baxter equation, from which commuting transfer matrices may be constructed. …”
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Staggered and affine Kac modules over A1(1) by Jørgen Rasmussen

“…This work concerns the representation theory of the affine Lie algebra A1(1) at fractional level and its links to the representation theory of the Virasoro algebra. …”
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Colored Tensor Models - a Review by Razvan Gurau, James P. Ryan

“…These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), non-trivial classical solutions and so on. …”
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Discrete Minimal Surface Algebras by Joakim Arnlind, Jens Hoppe

“…After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself). …”
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The Fourier U(2) Group and Separation of Discrete Variables by Kurt Bernardo Wolf, Luis Edgar Vicent

“…Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4). Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle) coordinates, thus realizing one case of separation in two discrete coordinates. …”
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SU(2) symmetry of coherent photons and application to Poincaré rotator by Shinichi Saito

“…Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. …”
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Quantum algorithms for generator coordinate methods by Muqing Zheng, Bo Peng, Nathan Wiebe, Ang Li, Xiu Yang, Karol Kowalski

“…The GCM formalism defined by exponential operators with exponents defined through generators of the fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of probing large subspaces using low-depth quantum circuits. …”
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A classification of real and complex nilpotent orbits of reductive groups in terms of complex even nilpotent orbits by Speh, Peter (Peter Daniel)

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Pure gravities via color-kinematics duality for fundamental matter by Ochirov, A, Johansson, H

“…We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.…”

On the weak N-dependence of SO(N) and SU(N) gauge theories in 2 + 1 dimensions by Athenodorou, A, Lau, R, Teper, M

“…We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N) and SU(N') theories and the equivalence of SO(∞) and SU(∞). …”

Interactions of strings on a T-fold by Yuji Satoh, Yuji Sugawara

“…Our results rely only on general properties of the asymmetric orbifold by the T-duality twist and of the Lie algebra lattice from the symmetry enhancement, and thus may be extended qualitatively to more general T-folds.…”
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Chirality, a new key for the definition of the connection and curvature of a Lie-Kac superalgebra by Jean Thierry-Mieg

“…Abstract A natural generalization of a Lie algebra connection, or Yang-Mills field, to the case of a Lie-Kac superalgebra, for example SU(m/n), just in terms of ordinary complex functions and differentials, is proposed. …”
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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. …”
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