Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem by Franchi Bruno, Marchi Marco, Serapioni Raul Paolo

“…A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. …”
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Symmetries and Solutions for a Class of Advective Reaction-Diffusion Systems with a Special Reaction Term by Mariano Torrisi, Rita Tracinà

“…The reaction term appearing in the equation for the species <i>v</i> is a logistic function of Lotka-Volterra type. Once obtained the Lie algebra for any form of <i>f</i> and <i>g</i> a Lie classification is carried out. …”
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A toy model for background independent string field theory by Maxim Grigoriev, Adiel Meyer, Ivo Sachs

“…Tensoring with a given Lie algebra results in a non-abelian extension of the model.…”
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On the Hamiltonian and geometric structure of Langmuir circulation by Yang, Cheng

“…We show that the CL equation can be reduced to the dual space of a certain Lie algebra central extension. On this space, the CL equation can be rewritten as a Hamiltonian equation corresponding to the kinetic energy. …”
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Centres of skewfields and completely faithful Iwasawa modules by Ardakov, K

“…Let H be a torsionfree compact p-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra \Lambda_H of H has trivial centre and use this result to classify the prime c-ideals in the Iwasawa algebra \Lambda_G of G := H \times \Zp. …”

Symplectic implosion and the Grothendieck-Springer resolution by Safronov, P

“…We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. …”

Holomorphic Dirichlet forms on complex manifolds by Gross, L, Qian, Z

“…They are classified in terms of the Lie algebra of the automorphism group, which we take to act in the unit ball of ℂ n. …”

Symmetry transformation of solutions for the navier-stokes equations by Fakhar, Kamran, Hayat, Tasawar K., Yi, Cheng Ging, Zhao, Kun Y.

“…It is shown in this study that the Navier-Stokes equations allows an infinite-dimensional Lie group of symmetries, i.e., a group transforming solutions amongst each other. The Lie algebra of this symmetry group here depends on four arbitrary functions of time. …”

On Lie Symmetries of Hyperbolic Model Metric of SL(n, R) Geometry by Rohollah Bakhshandeh Chamazkoti

“…As a more discussion in Lie algebra analysis‎, ‎one may find the Lie algebra of‎ Lie point symmetry corresponding to the metric is not semisimple or not solvable‎, because it has degenerated Killing form‎. …”
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Hidden symmetries of deformed oscillators by Sergey Krivonos, Olaf Lechtenfeld, Alexander Sorin

“…We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. …”
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Centrally extended BMS4 Lie algebroid by Glenn Barnich

“…Abstract We explicitly show how the field dependent 2-cocycle that arises in the current algebra of 4 dimensional asymptotically flat spacetimes can be used as a central extension to turn the BMS4 Lie algebra, or more precisely, the BMS4 action Lie algebroid, into a genuine Lie algebroid with field dependent structure functions. …”
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Double-soft graviton amplitudes and the extended BMS charge algebra by Jacques Distler, Raphael Flauger, Bart Horn

“…The commutator is expected to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the Virasoro algebra of local superrotations. …”
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Fibonacci, Golden Ratio, and Vector Bundles by Noah Giansiracusa

“…By computing the rank of the exceptional Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">g</mi><mn>2</mn></msub></semantics></math></inline-formula> case of these bundles in three different ways, a family of summation formulas for Fibonacci numbers in terms of the golden ratio is derived.…”
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Representations of U(2∞) and the Value of the Fine Structure Constant by William H. Klink

“…The fermion-antifermion operators generate a unitary Lie algebra, whose representations are fixed by a first order Casimir operator (corresponding to baryon number or charge). …”
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Geometric action for extended Bondi-Metzner-Sachs group in four dimensions by Glenn Barnich, Kevin Nguyen, Romain Ruzziconi

“…For any Hamiltonian associated with an extended BMS4 generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS4 Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. …”
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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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Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy by Panagiota Adamopoulou, Georgios Papamikos

“…The construction of the hierarchy and its conservation laws is based on the Drinfel'd-Sokolov scheme, however, in our case the Lax operator contains a constant non-regular element of the underlying Lie algebra. We also derive the associated recursion operator of the hierarchy using the symmetry structure of the Lax operators. …”
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Loop groups and diffeomorphism groups of the circle as colimits by Henriques, A

“…We use the above results to construct a comparison functor from the representations of a loop group conformal net to the representations of the corresponding affine Lie algebra. We also establish an equivalence of categories between solitonic representations of the loop group conformal net, and locally normal representations of the based loop group.…”

On isomorphism classes and invariants of a subclass of low-dimensional complex filiform Leibniz algebras by Rakhimov, Isamiddin Sattarovich, Said Husain, Sharifah Kartini

“…The first source is a naturally graded non-Lie filiform Leibniz algebra, and another one is a naturally graded filiform Lie algebra. In this article, we classify a subclass of the class of filiform Leibniz algebras appearing from the naturally graded non-Lie filiform Leibniz algebra. …”
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Lie-Poisson gauge theories and κ-Minkowski electrodynamics by V. G. Kupriyanov, M. A. Kurkov, P. Vitale

“…Abstract We consider gauge theories on Poisson manifolds emerging as semiclassical approximations of noncommutative spacetime with Lie algebra type noncommutativity. We prove an important identity, which allows to obtain simple and manifestly gauge-covariant expressions for the Euler-Lagrange equations of motion, the Bianchi and the Noether identities. …”
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