Post-Lie Algebra Structures on the Lie Algebra gl(2,C) by Yuqiu Sheng, Xiaomin Tang

“…The post-Lie algebra is an enriched structure of the Lie algebra. …”
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On whitehead's second lemma for Lie algebras by William T. Fletcher

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On the classification of the Lie algebras Lr,ts by L. A-M. Hanna

“…The Lie algebras Lr,ts introduced by the author (2003) are classified from an algebraic point of view. …”
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Graded radical W type Lie algebras I by Ki-Bong Nam

“…We get a new ℤ-graded Witt type simple Lie algebra using a generalized polynomial ring which is the radical extension of the polynomial ring F[x] with the exponential function ex.…”
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On the Exterior Degree of a Finite-Dimensional Lie Algebra by Afsaneh Shamsaki, Mohsen Parvizi, Ahmad Erfanian

“…In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field Fq and give upper and lower bounds. …”
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Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9 by Mercedes Pérez, Francisco P. Pérez, Emilio Jiménez

“…On the basis of the family of quasifiliform Lie algebra laws of dimension 9 of 16 parameters and 17 constraints, this paper is devoted to identify the invariants that completely classify the algebras over the complex numbers except for isomorphism. …”
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Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension by L. Magnin

“…We present tables for adjoint and trivial cohomologies of complex nilpotent Lie algebras of dimension . Attention is paid to quadratic Lie algebras, Poincaré duality, and harmonic cocycles.…”
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New Applications of a Kind of Infinitesimal-Operator Lie Algebra by Honwah Tam, Yufeng Zhang, Xiangzhi Zhang

“…Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. …”
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The Matrix Representations of Centroids for Low-Dimensional Mock-Lie Algebras by Yue Zhu, Keli Zheng

“…Mock-Lie algebras, a unique class of commutative algebras that satisfy the Jacobi identity, are gaining attention for their potential applications in various mathematical contexts. …”
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Solving Quantum Dynamics with a Lie-Algebra Decoupling Method by Sofia Qvarfort, Igor Pikovski

“…As background, we include an overview of Lie groups and Lie algebras aimed at a general-physicist audience. We then prove the Lie-algebra decoupling theorem and apply it to both closed and open dynamics. …”
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Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability by Muhammad Ayub, Masood Khan, F. M. Mahomed

“…We present a systematic procedure for the determination of a complete set of kth-order (k≥2) differential invariants corresponding to vector fields in three variables for three-dimensional Lie algebras. In addition, we give a procedure for the construction of a system of two kth-order ODEs admitting three-dimensional Lie algebras from the associated complete set of invariants and show that there are 29 classes for the case of k = 2 and 31 classes for the case of k≥3. …”
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Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras by Dan Chen, Xiao-Song Peng, Chia Zargeh, Yi Zhang

“…In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras, and matching pre-Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures.…”
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Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach by C. F. Lo, C. H. Hui

“…We present a Lie algebraic technique for the valuation of multi-asset financial derivatives with time-dependent parameters. …”
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Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation by G. Loaiza, Y. Acevedo, O.M.L. Duque, Danilo A. García Hernández

“…Finally, we classify the Lie algebra associated with the given equation.…”
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The Classification, Automorphism Group, and Derivation Algebra of the Loop Algebra Related to the Nappi–Witten Lie Algebra by Xue Chen

“…Then, L is called the loop Nappi–Witten Lie algebra. R-isomorphism classes of S/R forms of L are classified. …”
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A Family of Integrable Differential-Difference Equations: Tri-Hamiltonian Structure and Lie Algebra of Vector Fields by Ning Zhang, Xi-Xiang Xu

“…Next, a nonisospectral integrable family associated with the discrete spectral problem is constructed through nonisospectral discrete zero curvature representation. Finally, Lie algebra of isospectral and nonisospectral vector fields is deduced.…”
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Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 by S. V. Bolokhov, V. D. Ivashchuk

“…We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. …”
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Invariant Operators of Five-Dimensional Nonconjugate Subalgebras of the Lie Algebra of the Poincaré Group P(1,4) by Vasyl Fedorchuk, Volodymyr Fedorchuk

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Implementation of finite state logic machines via the dynamics of atomic systems by Dawit Hiluf Hailu

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Curtright-Zachos supersymmetric deformations of the Virasoro algebra in quantum superspace and Bloch electron systems by Haru-Tada Sato

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