Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables by Andronikos Paliathanasis

“…It is found that the admitted symmetries for the two sets of variables form different Lie algebras, leading to distinct one-dimensional optimal systems. …”
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On Orbits of Order Ideals of Minuscule Posets by David B. Rush, Xiaolin Shi

“…An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras. For these minuscule posets, it is shown that the Fon-Der-Flaass action exhibits the cyclic sieving phenomenon, as defined by Reiner, Stanton, and White. …”
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The SO(2r)2 string functions as q-diagrams by Arel Genish, Doron Gepner

“…We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the SO(2r) algebra. …”
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Recent Advances in Analytical Methods in Mathematical Physics by Ozer, Teoman, Taranov, Vladimir B., Smirnov, Roman G., Klemas, Thomas J., Thamburaja, Prakash, Wijesinghe, Sanith, Polat, Burak

“…We aimed to compile contributions across a variety of disciplines in mathematical physics such as integrability and chaos in dynamical systems, nonlinear partial differential equations, nonlinear problems in mechanics, control theory, geometrical methods, plasma physics, Lie algebras and representation theory, and statistical mechanics.…”
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Recurrence relations and path representations of matrix elements of an SU(1,1) algebra by Sukumar, C

“…A normal ordered representation of a Unitary operator $U$ constructed from the generators of a SU(1,1) algebra, which is a generalisation of the Baker- Campbell - Hausdorff relation for Lie algebras, is given. It is shown that the normal ordered representatiion of $U$ may be used to calculate expectation values which are functions of the parameters used to construct the operator. …”

Tadpoles and gauge symmetries by Andreas P. Braun, Bernardo Fraiman, Mariana Graña, Severin Lüst, Héctor Parra De Freitas

“…By working out possible gauge algebras for different values of the tadpole, we find that all simple ADE Lie algebras of rank ≤ 18 appear.…”
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On split involutive regular BiHom-Lie superalgebras by Guo Shuangjian, Zhang Xiaohui, Wang Shengxiang

“…The goal of this paper is to examine the structure of split involutive regular BiHom-Lie superalgebras, which can be viewed as the natural generalization of split involutive regular Hom-Lie algebras and split regular BiHom-Lie superalgebras. …”
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A uniform realization of the combinatorial $R$-matrix by Cristian Lenart, Arthur Lubovsky

“…Kirillov-Reshetikhin (KR) crystals are colored directed graphs encoding the structure of certain finite-dimensional representations of affine Lie algebras. A tensor product of column shape KR crystals has recently been realized in a uniform way, for all untwisted affine types, in terms of the quantum alcove model. …”
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Fun with F24 by Sarah M. Harrison, Natalie M. Paquette, Daniel Persson, Roberto Volpato

“…The models depend on the choice of an N $$ \mathcal{N} $$ = 1 supercurrent on F 24, with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how F 24, with any such choice of supercurrent, can be obtained via orbifolding from another distinguished c = 12 holomorphic SCFT, the N $$ \mathcal{N} $$ = 1 supersymmetric version of the chiral CFT based on the E 8 lattice.…”
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Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras by T. Chtioui, S. Mabrouk, A. Makhlouf

“…Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. …”
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Momentum conserving defects in affine Toda field theories by Rebecca Bristow, Peter Bowcock

“…Momentum conserving defects and Bäcklund transformations for affine Toda field theories based on the A n , B n , C n and D n series of Lie algebras are found. The defect associated with the D 4 affine Toda field theory is examined in more detail. …”
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Overlaps and fermionic dualities for integrable super spin chains by Charlotte Kristjansen, Dennis Müller, Konstantin Zarembo

“…The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. …”
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Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 $$ \mathcal{N}=4 $$ theories by Amihay Hanany, Marcus Sperling

“…Abstract The Coulomb branches of certain 3-dimensional N=4 $$ \mathcal{N}=4 $$ quiver gauge theories are closures of nilpotent orbits of classical or exceptional Lie algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular hyper-Kähler structure. …”
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Rectangular W-algebras of types so(M) and sp(2M) and dual coset CFTs by Thomas Creutzig, Yasuaki Hikida, Takahiro Uetoko

“…We compute the central charges of the algebras and the levels of so(M) or sp(2M) affine subalgebras by applying the Hamiltonian reductions of so or sp type Lie algebras. For simple cases with generators of spin up to two, we obtain their operator product expansions by requiring the associativity. …”
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Sampling the time evolution of mixed quantum-classical systems by Alessandro Sergi

“…In order to perform calculations, one can renounce to the usual Lie algebraic structure of well-established physical theories, adopt non-Hamiltonian brackets, and obtain a formalism for the dynamics and statistics of quantum-classical systems that has an affordable computational complexity. …”
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Group Analysis of the Plane Steady Vortex Submodel of Ideal Gas with Varying Entropy by Salavat Khabirov

“…The optimal systems of dissimilar subalgebras were obtained for the Lie algebras from the group classification. The example of the invariant vortex motion from the point source or sink was done. …”
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sl(2)ˆ Decomposition of denominator formulae of some BKM Lie superalgebras - II by Suresh Govindarajan, Mohammad Shabbir

“…We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for N=5,6.…”
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Dynamical equations of multibody systems on Lie groups by Wenjie Yu, Zhenkuan Pan

“…In this article, it is applied to derive a hybrid set of dynamical equations of rigid multibody systems, which include four parts: the classical Euler–Lagrange equations of rigid bodies in their translational coordinates of mass center; Euler–Poinaré equations via orientation matrices and their related angular velocities; the constraint equations due to different joints in Cartesian coordinates and Lie groups; and the reconstruction equations between special orthogonal groups and their Lie algebras. The generalized mass matrices of dynamical equations are constant, which is computationally efficient. …”
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The Lubin–Tate theory of configuration spaces: I by Brantner, L, Hahn, J, Knudsen, B

“…We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava <em>E</em>-theory, of unordered configuration spaces and identify its E²-page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the <em>E</em>-theory of the weight <em>p</em> summands of iterated loop spaces of spheres (parametrising the weight <em>p</em> operations on 𝔼_<em>n</em>-algebras), as well as the <em>E</em>-theory of the configuration spaces of <em>p</em> points on a punctured surface. …”

The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions by Lau, R, Teper, M

“…We also compare the deconfining temperatures of SO(6) with SU(4), and of SO(4) with SU(2) × SU(2), motivated by the fact that these pairs of gauge theories share the same Lie algebras.</p> …”