Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type by Ardakov, K, Wei, F, Zhang, J

“…Let $\Phi$ be a root system and let $\Phi(\Zp)$ be the standard Chevalley $\Zp$-Lie algebra associated to $\Phi$. For any integer $t\geq 1$, let $G$ be the uniform pro-$p$ group corresponding to the powerful Lie algebra $p^t \Phi(\Zp)$ and suppose that $p\geq 5$. …”

Algebraic representation of three qubit quantum circuit problems by Chew, K. Y., Shah, N. M., Chan, K. T.

“…To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. …”
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On isomorphism criteria for Leibniz central extensions of a linear deformation of mu_n. by Sattarovich, Rakhimov Isamiddin, Hassan, Munther A.

“…This paper deals with the classification problems of Leibniz central extensions of linear deformations of a Lie algebra. It is known that any n-dimensional filiform Lie algebra can be represented as a linear deformation of n-dimensional filiform Lie algebra μ n given by the brackets [e i, e 0] = e i+1, i = 0,1,⋯,n-2, in a basis {e 0, e 1,⋯,e n-1}. …”
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Connections on trivial vector bundles over projective schemes by Biswas, Indranil, Hô Hai, Phùng, dos Santos, Joao Pedro

“…In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial vector bundles and replacing the fundamental group by a certain Lie algebra constructed from the regular forms. In more detail, we show that the differential Galois group is a certain “closure” of the aforementioned Lie algebra.…”
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On Representations of sl(n, C) Compatible with a Z2-grading by M. Havlíček, E. Pelantová, J. Tolar

“…<p>This paper extends existing Lie algebra representation theory related to Lie algebra gradings. …”
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A Novel Coarse Alignment Method for SINS Using Special Orthogonal Group Optimal Estimation by Fujun Pei, Yang Su, Desen Zhu, Shunan Yin

“…Second is that a novel optimal estimation method is developed by using the exact error Lie algebra, which is calculated based on the physical definition of Lie algebra, as the innovation term to compensate the initial special orthogonal group in the estimation process. …”
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Motivic coaction and single-valued map of polylogarithms from zeta generators by Frost, H, Hidding, M, Kamlesh, D, Rodriguez, C, Schlotterer, O, Verbeek, B

“…We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. …”

Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry by K. S. Mahomed, E. Momoniat

“…It is shown that the maximal Lie algebra of a first integral for the simplest equation y′′′=0 is unique and four-dimensional. …”
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Some Results on Equivalence Groups by J. C. Ndogmo

“…In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group.…”
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Symmetries of quaternionic Kähler manifolds with S1‐symmetry by V. Cortés, A. Saha, D. Thung

“…More specifically, we study the metrics obtained by the one‐loop deformation of the c‐map construction, proving that the Lie algebra of infinitesimal automorphisms of the initial projective special Kähler manifold gives rise to a Lie algebra of Killing fields of the corresponding one‐loop deformed c‐map space. …”
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Periodic solutions and symmetry reductions of a generalized Chaffee–Infante equation by I. Humbu, B. Muatjetjeja, T.G. Motsumi, A.R. Adem

“…It will be shown that a generalized Chaffee–Infante equation admits four principal Lie algebra. It will be further shown that the principal Lie algebra admits only one possible extension. …”
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces by Oksana Ye. Hentosh

“…The existence problem of a Hamiltonian representation for the coupled Lax-type hierarchy on a dual space to the central extension of the shift operator Lie algebra is solved also.…”
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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation by Andrew Gratien Johnpillai, Chaudry Masood Khalique

“…The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. …”
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The Lie Group in Infinite Dimension by V. Tryhuk, V. Chrastinová, O. Dlouhý

“…A Lie group acting on finite-dimensional space is generated by its infinitesimal transformations and conversely, any Lie algebra of vector fields in finite dimension generates a Lie group (the first fundamental theorem). …”
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Correlated dynamics of immune network and sl(3, R) symmetry algebra by Dutta Ruma, Stan Aurel

“…We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. …”
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Yang–Baxter maps, discrete integrable equations and quantum groups by Vladimir V. Bazhanov, Sergey M. Sergeev

“…For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang–Baxter equation. …”
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Supersymmetric BKP systems and their symmetries by Chuanzhong Li, Jingsong He

“…These additional flows constitute a B type SW1+∞ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy. …”
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Representations having vectors fixed by a Levi subgroup associated to a real form by Smilga, I

“…For any semisimple real Lie algebra gR, we classify the representations of gR that have at least one nonzero vector on which the centralizer of a Cartan subspace, also known as the centralizer of a maximal split torus, acts trivially. …”

Note on the group of vertical diffeomorphisms of a principal bundle & its relation to the Frölicher-Nijenhuis bracket by J. François

“…The former is generated by the group of maps with value in the structure group, which is also the group of bisections of the groupoid. The corresponding Lie algebra of general vertical vector fields is generated by maps with value in the Lie algebra of the structure group. …”
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New Examples of Einstein Metrics in Dimension Four by Ryad Ghanam

“…We construct new examples of four-dimensional Einstein metrics with neutral signature and two-dimensional holonomy Lie algebra.…”
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