Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy by Oğul Esen, Miroslav Grmela, Hasan Gümral, Michal Pavelka

“…Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. …”
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A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism by Xinming Huo, Shuofei Yang, Binbin Lian, Tao Sun, Yimin Song

“…On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. …”
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Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs by Marc Geiller, Florian Girelli, Christophe Goeller, Panagiotis Tsimiklis

“…Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an algebra of vector fields. …”
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Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra by Martin Cederwall, Jakob Palmkvist

“…We apply it to cases where a grey node is added to the Dynkin diagram of a rank r + 1 Kac-Moody algebra g $$ \mathfrak{g} $$ +, which in turn is an extension of a rank r finite-dimensional semisimple simply laced Lie algebra g $$ \mathfrak{g} $$ . The algebras are specified by g $$ \mathfrak{g} $$ together with a dominant integral weight λ. …”
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A Lie group variational integrator in a closed-loop vector space without a multiplier by L. Bai, L. Xia, X. Ge

“…The kinematic constraint variation relation of a closed-loop system is built in matrix and vector space with Lie group and Lie algebra theory respectively. The results indicate that the attitude variation between the driven body and the follower body has a linear recursion relation, which is the basis for dynamics modelling. …”
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Microscopic description of odd-odd transitional nuclei by using interacting-boson-fermion -model by M. Ghapanvari, N. Amiri, M.A. Jafarizadeh, H. Hossein Khani

“…In this paper, solvable algebraic models by using the affine SU(1,1) Lie Algebra and proton, and neutron degrees of freedom in the framework of an  interacting-boson-fermion-fermion model(IBFFM) is suggested to determine the exact energy and eigenstate of the  transitional odd-odd mass nuclei. …”
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Quiver theories and formulae for Slodowy slices of classical algebras by Santiago Cabrera, Amihay Hanany, Rudolph Kalveks

“…We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra g. We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone S∩N of g. …”
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Symmetry reductions and invariant-group solutions for a two-dimensional Kundu–Mukherjee–Naskar model by Rodica Cimpoiasu, Hadi Rezazadeh, Daniela Aurelia Florian, Hijaz Ahmad, Kamsing Nonlaopon, Mohamed Altanji

“…We took the full advantages of the Lie symmetry method, concluding that the model admits a 7D Lie algebra. Using the similarity reduction method, we have successfully obtained various kinds of complex-valued wave solutions with hyperbolic-, periodic-, rational-, general-function amplitudes. …”
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Qudit-Basis Universal Quantum Computation Using X[superscript (2)] by Niu, Yuezhen, Chuang, Isaac, Shapiro, Jeffrey H

“…Next, we demonstrate qutrit-basis universality by proving that χ[superscript (2)] Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ[superscript (2)] interactions. …”
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Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K by Bakalov, Bojko, D’Andrea, Alessandro, Kac, Victor

“…A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra. The finite (i.e.,finitely generated over H) simple Lie pseudoalgebras were classified in our previous work (Bakalov etal., 2001) [2] . …”
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Gaudin model and Deligne’s category by Feigin, B., Rybnikov, L., Uvarov, F.

“…We show that the construction of the higher Gaudin Hamiltonians associated with the Lie algebra $$\mathfrak {gl}_{n}$$ gl n admits an interpolation to any complex number n. …”
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Genus expansion of matrix models and $$\hbar $$ ħ expansion of BKP hierarchy by Yaroslav Drachov, Aleksandr Zhabin

“…In this paper, we focus on the BKP hierarchy, which corresponds to the infinite-dimensional Lie algebra of type B. We consider the genus expansion of such important solutions as Brézin–Gross–Witten (BGW) model, Kontsevich model, and generating functions for spin Hurwitz numbers with completed cycles. …”
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The solution of equations of ideal gas that describes Galileo invariant motion with helical level lines, with the collapse in the helix by Yuliya Valer'evna Yulmukhametova

“…We consider the equations of ideal gas dynamics in a cylindrical coordinate system with the arbitrary equation of state and one two-dimensional subalgebra from the optimum system of an 11-dimensional Lie algebra of differentiation operators of the first order. …”
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The spectrum properties of an integrable G2 invariant vertex model by M.J. Martins

“…The model R-matrix and respective spin chain are presented in terms of the basis generators of the G2 Lie algebra. This formulation permits us to relate the number of the Bethe roots of the respective Bethe equations with the eigenvalues of the U(1) conserved charges from the Cartan subalgebra of G2. …”
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The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory by Maximilian Rupprecht

“…We propose a general theory of the N $$ \mathcal{N} $$ = 4 coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra su $$ \mathfrak{su} $$ (4). This theory incorporates our two construction approaches as special points in su $$ \mathfrak{su} $$ (4) and defines a broad class of Nicolai maps for N $$ \mathcal{N} $$ = 4 SYM.…”
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Wilson loops in N $$ \mathcal{N} $$ = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5 by Simone Giombi, Bendeguz Offertaler

“…By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5 × ℝℙ5. …”
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The role of positivity and causality in interactions involving higher spin by Bert Schroer

“…These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H.The basic conceptual and calculational tool of SLFT is the S-matrix. …”
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Whole brain volume changes and its correlation with clinical symptom severity in patients with schizophrenia: A DARTEL-based VBM study. by Gwang-Won Kim, Yun-Hyeon Kim, Gwang-Woo Jeong

“…Magnetic resonance image data were processed using SPM8 software with diffeomorphic anatomical registration via an exponentiated Lie algebra (DARTEL) algorithm. Patients with schizophrenia exhibited significantly decreased GM volumes of the insula, superior temporal gyrus (STG), gyrus rectus, and anterior cingulate cortex (ACC) compared with healthy controls. …”
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Twistors, the ASD Yang-Mills equations and 4d Chern-Simons theory by Roland Bittleston, David Skinner

“…Examples include a 4d analogue of the Wess-Zumino-Witten model and a theory of a Lie algebra valued scalar with a cubic two derivative interaction. …”
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SYMMETRIES AND LAX INTEGRABILITY OF THE GENERALIZED PROUDMAN-JOHNSON EQUATION by O. I. Morozov

“…In particular, if <р is a characteristic of a symmetry for a PDE Н = О then the <р-invariant solution of the PDE is a solution to the compatible over-determined system Н = О, < р = О. We show that the Lie algebra of local symmetries for the generalized Proudman-Johnson equation is infinite-dimensional. …”
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