Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives by Aldandani Mohammed, Rizvi Syed T. R., Alruwaili Abdulmohsen, Seadawy Aly R.

“…Solitons have extensive uses in pure and applied mathematics, including nonlinear partial differential equations: the Boussinesq equation, the nonlinear Schrödinger equation, and the sine-Gordon equation, Lie groups, Lie algebras, and differential and algebraic geometry. …”
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On algebraic singularities, finite graphs and D-brane gauge theories : a string theoretic perspective -- with a digression on string field theory by He, Yang-Hui, 1975-

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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras by Tsymbaliuk, Oleksandr

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On Auslander-Reiten theory for algebras and derived categories by Scherotzke, S

“…We apply these results to <em>G</em>-transitive blocks of the universal enveloping algebras of restricted <em>p</em>-Lie algebras. Finally we deduce a condition for a smash product of a local basic algebra Λ with a commutative semi-simple group algebra to have components with Euclidean tree class, in terms of the components of the Auslander-Reiten quiver of Λ.…”

Configurations in abelian categories. III. Stability conditions and identities by Joyce, D

“…Using these we define interesting (Lie) algebras of constructible functions H^{pa}_t,H^{to}_t and L^{pa}_t,L^{to}_t on Obj_A. …”

Configurations in abelian categories. II. Ringel-Hall algebras by Joyce, D

“…Under extra conditions on A we can define (Lie) algebra morphisms from SF(Obj_A) to some explicit (Lie) algebras, which will be important in the sequels on invariants counting t-(semi)stable objects in A.…”

Non-finitary Generalizations of Nil-triangular Subalgebras of Chevalley Algebras by J. V. Bekker, V. M. Levchuk, E. A. Sotnikova

“…Well-known (1990) special matrix representation of Lie algebras $N\Phi(K)$ allows to construct non-finitary generalizations $NG(K)$ of type $G=B_\Gamma,C_\Gamma$ and $D_\Gamma$. …”
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Poisson traces, D-modules, and symplectic resolutions by Schedler, Travis, Etingof, Pavel I

“…We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein–Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. …”
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A Hybrid Approach Combining the Lie Method and Long Short-Term Memory (LSTM) Network for Predicting the Bitcoin Return by Melike Bildirici, Yasemen Ucan, Ramazan Tekercioglu

“…The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. …”
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Integrability of rank-two web models by Augustin Lafay, Azat M. Gainutdinov, Jesper Lykke Jacobsen

“…These models are based on the A2, G2 and B2 Lie algebras, and their local vertex configurations are intertwiners of the corresponding q-deformed quantum algebras. …”
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Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators by Alekseev, Anton, Naef, Florian, Zhu, Chenchang, Xu, Xiaomeng

“…In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to ω[subscript 1]=C(F) . …”
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Coherent sheaves on varieties arising in Springer theory, and category 0 by Nandakumar, Vinoth

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Symplectic geometry of conical symplectic resolutions by Zivanovic, F

“…The family of Nakajima Quiver Varieties, in particular, we study in detail those of Dynkin type A; and the family of resolutions of Slodowy varieties that arise from the representation theory of semisimple Lie algebras and involve Springer theory. In the latter, we also obtain some further families of Lagrangians using Springer theoretic methods and certain crystal operators.…”

Solving Particle–Antiparticle and Cosmological Constant Problems by Felix M. Lev

“…The problem of why the quantities <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>c</mi><mo>,</mo><mo>ℏ</mo><mo>,</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. …”
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Rough paths, kernels, differential equations and an algebra of functions on streams by Salvi, C

“…The atomic objects in a) are described via different algebraic products and using classical combinatorial objects (Hall sets) arising in the study of free Lie algebras.</p> <p>[1] Franz J Király and Harald Oberhauser. …”

On 4-dimensional Einsteinian manifolds with parallel null distribution by Mehdi Jafari

“…Also, a complete analysis of this group and Lie algebras like it will be presented. In the fourth section, the optimal system of the one-parameter subalgebras of the symmetric algebra of Einstein's equations is presented, and then the reduced equations are obtained using differential derivations. …”
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Batalin-Vilkovisky formality for Chern-Simons theory by Ezra Getzler

“…Abstract We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. …”
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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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Isomorphism of Intransitive Linear Lie Equations by Jose Miguel Martins Veloso

“…Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. …”
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Conformal Embeddings and Simple Current Extensions by Frajria, Pierluigi Möseneder, Papi, Paolo, Xu, Feng, Kac, Victor

“…In this paper, we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.…”
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