Hom-Yang-Baxter Equations and Frobenius Monoidal Hom-Algebras by Yuanyuan Chen, Liangyun Zhang

“…It is shown that quasi-Frobenius Hom-Lie algebras are connected with a class of solutions of the classical Hom-Yang-Baxter equations. …”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. …”
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A construction of some ideals in affine vertex algebras by Draen AdamoviĆ

“…We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. …”
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On the Deformations and Derivations of n-Ary Multiplicative Hom-Nambu-Lie Superalgebras by Baoling Guan, Liangyun Chen, Yao Ma

“…As a generalization of the notion of derivations for n-ary multiplicative Hom-Nambu-Lie algebras, we discuss the derivations of n-ary multiplicative Hom-Nambu-Lie superalgebras. …”
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Dirac Equation on the Torus and Rationally Extended Trigonometric Potentials within Supersymmetric QM by Özlem Yeşiltaş

“…In addition, using the aspects of the Lie algebraic approaches, the iso(2,1) algebra is also applied to the system where we have arrived at the spectrum solutions of the extended potentials using the Casimir operator that matches with the results of the exact solutions.…”
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TBA equations and quantum periods for D-type Argyres-Douglas theories by Katsushi Ito, Jingjing Yang

“…We study the variety of TBA systems across the Coulomb branch moduli space and find that they correspond to the Dynkin diagrams of D n Lie algebras in the minimal chamber, and reproduce the TBA equations for reflectionless D scattering theories at the maximally symmetric point. …”
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Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups by Ángel Ballesteros, N. Rossano Bruno, Francisco J. Herranz

“…The Drinfel’d-double and the Poisson–Lie structure underlying the κ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the κ-Minkowski space to the (anti-)de Sitter ones are obtained. …”
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Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields by Shun'ya Mizoguchi, Takumi Oikawa

“…This code-lattice construction is redescribed in terms of root and weight lattices of Lie algebras, which allows to construct lattices for codes over rings Zq with non-prime q. …”
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Locally conformal symplectic manifolds by Izu Vaisman

“…Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. …”
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