On lie-like filiform Leibniz algebras. by Omirov, B. A., Sattarovich, Rakhimov Isamiddin

“…This subclass arises from the naturally graded filiform Lie algebras. We reconcile and simplify the structure constants of such a class. …”

Triality Groups Associated with Triple Systems and their Homotope Algebras by Kamiya Noriaki

“…We introduce the notion of an (α, β, γ) triple system, which generalizes the familiar generalized Jordan triple system related to a construction of simple Lie algebras. We then discuss its realization by considering some bilinear algebras and vice versa. …”
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On the Virasoro Structure of Symmetry Algebras of Nonlinear Partial Differential Equations by Faruk Güngör

“…We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts. …”
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Deformations of spacetime and internal symmetries by Gresnigt Niels G., Gillard Adam B.

“…The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. …”
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Symmetry-induced decoherence-free subspaces by Jonathan Dubois, Ulf Saalmann, Jan Michael Rost

“…Constructing them is facilitated in classical phase space and can be transferred to quantum mechanics through the equivalent role that Poisson and Lie algebras play for symmetries in classical and quantum mechanics, respectively. …”
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Bethe/Gauge correspondence for ABCDEFG-type 3d gauge theories by Xiang-Mao Ding, Tinglyer Zhang

“…Especially, for exceptional Lie algebras F4, G2, we give the effective superpotential and vacuum equations. …”
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Intertwining Symmetry Algebras of Quantum Superintegrable Systems by Juan A. Calzada, Javier Negro, Mariano A. del Olmo

“…We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). …”
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On the symmetries of singular limits of spacetimes by Eric Bergshoeff, Javier Matulich, Tomás Ortín

“…We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves.…”
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Representation theory in complex rank, II by Etingof, Pavel I

“…Namely, we define complex rank analogs of the parabolic category O and the representation categories of real reductive Lie groups and supergroups, affine Lie algebras, and Yangians. We develop a framework and language for studying these categories, prove basic results about them, and outline a number of directions of further research. …”
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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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TANGENTIAL LOCALIZATION FOR SELMER VARIETIES by Kim, M

“…This paper proposes a tangential version of the theory of Selmer varieties together with a formulation of cohomological duality in families of Lie algebras indexed by nonabelian cohomology. This theory allows one to consider deformations of cohomology classes as one moves over the Selmer variety and suggests an approach for generalizing to number fields the homotopical techniques for proving Diophantine finiteness that were developed over Q{double-struck}. …”

Second Chern-Einstein metrics on four-dimensional almost-Hermitian manifolds by Barbaro Giuseppe, Lejmi Mehdi

“…Finally, we study the second Chern-Einstein problem on unimodular almost-abelian Lie algebras, classifying those that admit a left-invariant second Chern-Einstein metric with a parallel non-zero Lee form.…”
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Line operators of gauge theories on non-spin manifolds by J.P. Ang, Konstantinos Roumpedakis, Sahand Seifnashri

“…This is used to classify all possible sets of allowed line operators — including their spins — for gauge theories with simple Lie algebras. The Lagrangian descriptions of the theories with these sets of allowed line operators are given. …”
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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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Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function by Schilling, Anne, Tingley, Peter

“…It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. …”
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On universal quantum dimensions by R.L. Mkrtchyan

“…It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of adjoint and some other series of irreps of simple Lie algebras. These formulae also provide a proof of formulae for universal quantum dimensions for low-dimensional representations, needed in derivation of universal knot polynomials (i.e. colored Wilson averages of Chern–Simons theory on 3d sphere). …”
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Symmetric degenerations are not in general induced by type A degenerations by Magdalena Boos, Giovanni Cerulli Irelli

“…In connection with Borel orbits of 2-nilpotent matrices of classical Lie algebras, we describe an explicit example of a quiver of finite representation type for which orbit closure relations are induced in types B and C, but not in type D.…”
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Continuous-time quantum harmonic oscillator state engineering by E García Herrera, F Torres-Leal, B M Rodríguez-Lara

“…We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.…”
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Complete solution to Gaussian tensor model and its integrable properties by H. Itoyama, A. Mironov, A. Morozov

“…This is a part of the long-standing problem to define a non-Abelian lift of integrability from the fundamental to generic representation families of arbitrary Lie algebras.…”
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THE SOCCER-BALL PROBLEM IN QUANTUM SPACE by KHRYSTYNA P. GNATENKO, VOLODYMYR M. TKACHUK

“…It is shown that this problem can be solved in a deformed space with a minimal length, in a noncommutative phase space, in a space with a Lie-algebraic noncommutativity, in a twist-deformed space-time due to the relation of parameters of corresponding algebras with mass. …”
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