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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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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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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Prime ideals in noncommutative Iwasawa algebras by Ardakov, K

“…We study the prime ideal structure of the Iwasawa algebra ΛG of an almost simple compact p-adic Lie group G. When the Lie algebra of G contains a copy of the two-dimensional non-abelian Lie algebra, we show that the prime ideal structure of ΛG is somewhat restricted. …”

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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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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Depth-graded motivic multiple zeta values by Brown, F

“…We formulate a single conjecture about the homology of this Lie algebra which implies conjectures due to Broadhurst and Kreimer, Racinet, Zagier, and Drinfeld on the structure of multiple zeta values and on the Grothendieck–Teichmüller Lie algebra.…”

Formality in generalized Kähler geometry by Cavalcanti, G

“…We prove that no nilpotent Lie algebra admits an invariant generalized Kahler structure. …”

Rational structures on multiple zeta values by Keilthy, A

“…By considering the associated graded Lie algebra of the motivic Lie algebra with respect to this filtration, we obtain an isomorphic Lie algebra bg with canonical representatives for its generators in Q<e₀,e₁>. …”

On the Lie structure of locally matrix algebras by O. Bezushchak

“….$ We find a necessary and sufficient condition for the Lie algebra $A\diagup\mathbb{F}\cdot 1$ to be simple and for the Lie algebra of derivations $\text{Der}(A)$ to be topologically simple. …”
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Nonlinear Bi-Integrable Couplings of Multicomponent Guo Hierarchy with Self-Consistent Sources by Hongwei Yang, Huanhe Dong, Baoshu Yin, Zhenyu Liu

“…Based on a well-known Lie algebra, the multicomponent Guo hierarchy with self-consistent sources is proposed. …”
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Semilinear automorphisms of classical groups and quivers by Yang, Jinwei, Yun, Zhiwei

“…More precise classification is given when g is a loop Lie algebra, i.e., when F = ℂ((t)).…”
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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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