Three-dimensional hypergravity theories and semigroup expansion method by Ricardo Caroca, Patrick Concha, Javier Matulich, Evelyn Rodríguez, David Tempo

“…Abstract In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hypergravity theories. …”
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Universal Racah matrices and adjoint knot polynomials: Arborescent knots by A. Mironov, A. Morozov

“…By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso–Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. …”
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Generic character sheaves on groups over k[∊]/[∊]r by Lusztig, George

“…Let g, b, t, n be the Lie algebras of G, B, T, U. We fix a prime number l ≠ p. …”
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Duality twisted reductions of Double Field Theory of Type II strings by Aybike Çatal- Özer

“…We show that the set of conditions required for the consistency of the reduction of the NS-NS sector are also crucial for the consistency of the reduction of the RR sector, owing to the fact that the Lie algebras of Spin(n, n) and SO(n, n) are isomorphic. …”
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Discovering T-dualities of little string theories by Bhardwaj, L

“…For many, but not all, circle compactifications of N = (1, 1) little string theories, we have T-dualities that realize Langlands dualities between affine Lie algebras. Along the way, we find another discrete theta angle distinct from 0 and π for an E-string node.…”

Non-perturbative aspects of the self-dual double copy by Kymani Armstrong-Williams, Chris D. White, Sam Wikeley

“…In doing so, we demonstrate how the replacement of colour by kinematic Lie algebras operates at the level of exact classical solutions.…”
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An Ising-type formulation of the six-vertex model by Vladimir V. Bazhanov, Sergey M. Sergeev

“…Plausibly, all vertex models associated with quantized affine Lie algebras and superalgebras can be reformulated as Ising-type models with only two-spin interactions.…”
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Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions by Frassek, Rouven, Karpov, Ivan, Tsymbaliuk, Alexander

“…Abstract We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras $${\mathfrak {g}}$$ g , whose highest weight is a multiple of a fundamental one and which can be lifted to the representations over the Yangian $$Y({\mathfrak {g}})$$ Y ( g ) . …”
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Characterizations of Group Theory under Q-Neutrosophic Soft Environment by Majdoleen Abu Qamar, Nasruddin Hassan

“…Different extensions of fuzzy sets have been already implemented to several algebraic structures, such as groups, symmetric groups, rings and lie algebras. Group theory is one of the most essential algebraic structures in the field of algebra. …”
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The explicit molecular expansion of the combinatorial logarithm by Gilbert Labelle

“…The main goal of the present work is to fill this gap by computing explicitly the molecular expansion of the combinatorial logarithm and of $-\mathrm{Lg}(1-X)$, a "cousin'' of the tensorial species, $\mathrm{Lie}(X)$, of free Lie algebras.…”
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Discovering T-dualities of little string theories by Lakshya Bhardwaj

“…For many, but not all, circle compactifications of N $$ \mathcal{N} $$ = (1, 1) little string theories, we have T-dualities that realize Langlands dualities between affine Lie algebras. Along the way, we find another discrete theta angle distinct from 0 and π for an E-string node.…”
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Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications by Shun’ya Mizoguchi, Taro Tani

“…Among them, there are cases in which the MW lattice is none of the weight lattices of simple Lie algebras or direct sums thereof. We study how such “non-Cartan MW lattices” are realized in the six-dimensional heterotic/F-theory compactifications. …”
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Vertex operator algebras, Higgs branches, and modular differential equations by Beem, C, Rastelli, L

“…We illustrate these ideas in a number of examples including a series of rank-one theories associated with the “Deligne-Cvitanović exceptional series” of simple Lie algebras, several families of Argyres-Douglas theories, an assortment of class S theories, and N=2 super Yang-Mills with su(n) gauge group for small-to-moderate values of n.…”

Next-to-MHV Yang-Mills kinematic algebra by Gang Chen, Henrik Johansson, Fei Teng, Tianheng Wang

“…Abstract Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. …”
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Old Game, New Rules: Rethinking the Form of Physics by Christian Baumgarten

“…The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. …”
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Peculiarities of beta functions in sigma models by Oleksandr Gamayun, Andrei Losev, Mikhail Shifman

“…In addition to the generic Kähler target spaces we discuss in detail the so-called Lie-algebraic sigma models. In particular, this is the case when the perturbed field G i j ¯ $$ {G}^{i\overline{j}} $$ is a product of the holomorphic and antiholomorphic currents satisfying two-dimensional current algebra.…”
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Smiley Theorem for Spectral Operators Whose Radical Part Is Locally Nilpotent by Jianjian Jiang, Xiao Chen, Xiaolin Li

“…Generalizing bicommutant theorem to the higher-order commutator case is very useful for representation theory of Lie algebras, which plays an important role in symmetry analysis. …”
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Towards (3+1) gravity through Drinfel'd doubles with cosmological constant by Angel Ballesteros, Francisco J. Herranz, Pedro Naranjo

“…We present the generalisation to (3+1) dimensions of a quantum deformation of the (2+1) (Anti)-de Sitter and Poincaré Lie algebras that is compatible with the conditions imposed by the Chern–Simons formulation of (2+1) gravity. …”
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Construction of Deligne Categories through ultrafilters and its applications by Kalinov, Daniil

“…In Chapter 4 the full classification of simple commutative, associative and Lie algebras in Rep(𝑆𝜈) for 𝜈 /∈ Z≥0 is stated and proven. …”
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A (1 + 2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II by Roman Cherniha, Maksym Didovych

“…It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is presented. …”
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