A (1 + 2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II by Roman Cherniha, Maksym Didovych

“…It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is presented. …”
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Symmetries and Geometries of Qubits, and Their Uses by A. R. P. Rau

“…This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. …”
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Towards Unifying Structures in Higher Spin Gauge Symmetry by Anders K.H. Bengtsson

“…A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. …”
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Disconnected 0-form and 2-group symmetries by Lakshya Bhardwaj, Dewi S. W. Gould

“…Examples of arbitrarily complex disconnected 0-form and 2-group symmetries in any spacetime dimension are furnished by gauge theories: with 1-form symmetries arising from the center of the gauge group, continuous 0-form symmetries arising as flavor symmetries acting on matter content, and finite 0-form symmetries arising from outer-automorphisms of gauge and flavor Lie algebras.…”
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Quiver theories and Hilbert series of classical Slodowy intersections by Amihay Hanany, Rudolph Kalveks

“…The vacuum moduli spaces of many such theories can be parameterised by pairs of nilpotent orbits of Classical Lie algebras; they are transverse to one orbit and intersect the closure of the second. …”
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Physics of infinite complex structure limits in eight dimensions by Seung-Joo Lee, Wolfgang Lerche, Timo Weigand

“…As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. …”
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Generic character sheaves on groups over k[∊]/[∊]r by Lusztig, George

“…Let g, b, t, n be the Lie algebras of G, B, T, U. We fix a prime number l ≠ p. …”
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Supersymmetric gauge theories from D3-branes on singularities by Kazakopoulos, Pavlos

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Gröbner bases in rational homotopy theory by Lee, Wai Kei Peter

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The classification of delay differential equations using lie symmetry analysis by Muhsen, Laheeb

“…Consequently, these equations were studied via Lie algebraic classification to the specific case of second-order retarded DDEs (RDDEs). …”
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Three-dimensional hypergravity theories and semigroup expansion method by Ricardo Caroca, Patrick Concha, Javier Matulich, Evelyn Rodríguez, David Tempo

“…Abstract In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hypergravity theories. …”
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Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants by Alexander A. Balinsky, Denis Blackmore, Radosław Kycia, Anatolij K. Prykarpatski

“…We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. …”
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Energy-Preserving/Group-Preserving Schemes for Depicting Nonlinear Vibrations of Multi-Coupled Duffing Oscillators by Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang

“…The main novelty is that we constructed the quadratic forms of the energy equations, the Lie-algebras and Lie-groups for the multi-coupled Duffing oscillator system. …”
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Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature by Mozhey, Natalya Pavlovna

“…Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character. …”
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On a class of conformal E $$ \mathcal{E} $$ -models and their chiral Poisson algebras by Sylvain Lacroix

“…The case of degenerate E $$ \mathcal{E} $$ -models, in which a subalgebra of the current algebra is gauged, is more involved: the conformal condition yields a wider class of theories, which includes gauged WZW models but also other examples, seemingly different, which however sometimes turn out to be related to gauged WZW models based on other Lie algebras. For this class, we build non-local chiral fields of parafermionic-type as well as higher-spin local ones, forming classical W $$ \mathcal{W} $$ -algebras. …”
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Finite dimensional Hopf actions on algebraic quantizations by Etingof, Pavel I, Walton, Chelsea

“…This includes universal enveloping algebras of finite dimensional Lie algebras, spherical symplectic reflection algebras, quantum Hamiltonian reductions of Weyl algebras (in particular, quantized quiver varieties), finite W-algebras and their central reductions, quantum polynomial algebras, twisted homogeneous coordinate rings of abelian varieties, and Sklyanin algebras. …”
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Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions by Frassek, Rouven, Karpov, Ivan, Tsymbaliuk, Alexander

“…Abstract We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras $${\mathfrak {g}}$$ g , whose highest weight is a multiple of a fundamental one and which can be lifted to the representations over the Yangian $$Y({\mathfrak {g}})$$ Y ( g ) . …”
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The geometrical language of continuum mechanics / by Epstein, M. (Marcelo)

Quiver subtractions by Santiago Cabrera, Amihay Hanany

“…One is the extension of the physical realization of Kraft-Procesi transitions from the classical to the exceptional Lie algebras. Another result is the extension from special nilpotent orbits to non-special ones. …”
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New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations by Renata Nikonorova, Dilara Siraeva, Yulia Yulmukhametova

“…Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. …”
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