Rings with involution whose symmetric elements are central by Taw Pin Lim

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Differentiable semigroups are Lie groups by John P. Holmes, Mitch Anderson

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Spherical Harmonics Ylm(θ,ϕ): Positive and Negative Integer Representations of su(1,1) for l-m and l+m by H. Fakhri

“…So, in addition to realizing the unitary irreducible representation of su(2) compact Lie algebra via the Ylm(θ,ϕ)’s for a given l, we can also represent su(1,1) noncompact Lie algebra by spherical harmonics for given values of l-m and l+m.…”
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Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy by Zhengduo Shan, Hongwei Yang, Baoshu Yin

“…With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. …”
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Noether Symmetries of the Area-Minimizing Lagrangian by Adnan Aslam, Asghar Qadir

“…It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1)-area enclosing a constant n-volume in a Euclidean space is so(n)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). …”
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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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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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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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Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries by Fatemeh Ahangari

“…It is represented that the Lie algebra of local symmetries interrelated to the system of geodesic equations is non-solvable and not semi-simple and the algebraic organization of the derived quotient Lie algebra is accurately evaluated. …”
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Massive bigravity as a presymplectic BV-AKSZ sigma-model by Maxim Grigoriev, Vyacheslav Gritzaenko

“…A characteristic feature of the construction is that the target space is realised as a quasi-regular submanifold of a linear graded manifold which, in turn, is a direct product of two copies of the shifted Poincaré or (anti-)de Sitter Lie algebra. This graded manifold comes equipped with a natural presymplectcic structure and the compatible pre-Q structure which is a sum of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term. …”
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Sectional and Ricci Curvature for Three-Dimensional Lie Groups by Gerard Thompson, Giriraj Bhattarai

“…In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.…”
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On the Deformation Theory of Structure Constants for Associative Algebras by B. G. Konopelchenko

“…Deformations of associative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable systems are studied.…”
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Geometric Methods to Investigate Prolongation Structures for Differential Systems with Applications to Integrable Systems by Paul Bracken

“…They are based on a set of one forms for which the underlying structure group of the integrability condition corresponds to the Lie algebra of , , and . Each will be considered in turn and the latter two systems represent larger cases. …”
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Horadam Spinors by Tülay Erişir

“…Spinors can be expressed as Lie algebra of infinitesimal rotations. Spinors are also defined as elements of a vector space which carries a linear representation of the Clifford algebra typically. …”
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Multilocal invariants for the classical groups by Paul F. Dhooghe

“…The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.…”
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On the geometry of Riemannian manifolds with a Lie structure at infinity by Bernd Ammann, Robert Lauter, Victor Nistor

“…We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.…”
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Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution by H. Panahi, M. Baradaran

“…We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. …”
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Algebro-Geometric Solutions for a Discrete Integrable Equation by Mengshuang Tao, Huanhe Dong

“…With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. …”
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The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures by Juhui Zhang, Yuqin Yao

“…Furthermore, based on the semidirect sums of matrix Lie algebras consisting of 3×3 block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.…”
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Bi-Integrable Couplings of a New Soliton Hierarchy Associated with SO(4) by Yan Cao, Liangyun Chen, Baiying He

“…Based on the six-dimensional real special orthogonal Lie algebra SO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. …”
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