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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Discovering sparse representations of Lie groups with machine learning by Roy T. Forestano, Konstantin T. Matchev, Katia Matcheva, Alexander Roman, Eyup B. Unlu, Sarunas Verner

“…In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the U(n) and SU(n) families of Lie groups. …”
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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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Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties by R. J. Moitsheki, O. D. Makinde

“…Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of the arbitrary constants and the source term. …”
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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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Hodge decomposition of string topology by Yuri Berest, Ajay C. Ramadoss, Yining Zhang

“…We prove that the string topology bracket on the $S^1$-equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $, making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. …”
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Relations in Quantized Function Algebras by Etingof, Pavel I, Neshveyev, Sergey

“…In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie algebras. Keyword: Quantized function algebras; C*-tensor categories; Quantum groups at roots of unity; Quasitriangular Hopf algebras…”
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Moduli spaces of sheaves on surfaces: Hecke correspondences and representation theory by Neguţ, A

“…Its cohomology and intersection theory (as well as those of its more complicated cousins, the flag varieties) have long been studied in connection with the Lie algebras 𝔰 𝔩 n.…”
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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> …”

The spectrum of quantum-group-invariant transfer matrices by Rafael I. Nepomechie, Ana L. Retore

“…Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. …”
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On q-deformed infinite-dimensional n-algebra by Lu Ding, Xiao-Yu Jia, Ke Wu, Zhao-Wen Yan, Wei-Zhong Zhao

“…We find that they are the sh-n-Lie algebras for the n even case. In terms of the magnetic translation operators, an explicit physical realization of the (co)sine n-algebra is given.…”
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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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Symmetries in Classical and Quantum Treatment of Einstein’s Cosmological Equations and Mini-Superspace Actions by Theodosios Christodoulakis, Alexandros Karagiorgos, Adamantia Zampeli

“…The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. …”
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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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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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Intrinsic geometry and director reconstruction for three-dimensional liquid crystals by Joseph Pollard, Gareth P Alexander

“…Finally, we discuss the coupling between individual distortions and curvature from the perspective of Lie algebras and groups and describe homogeneous spaces on which pure modes of distortion can be realised.…”
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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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Galilean contractions of W-algebras by Jørgen Rasmussen, Christopher Raymond

“…We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. …”
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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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