A quantum framework for AdS/dCFT through fuzzy spherical harmonics on S 4 by Aleix Gimenez-Grau, Charlotte Kristjansen, Matthias Volk, Matthias Wilhelm

“…The classical fields have commutators which constitute an irreducible representation of the Lie algebra so $$ \mathfrak{so} $$ (5) leading to a highly non-trivial mixing between color and flavor components of the quantum fields. …”
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Correspondences among CFTs with different W-algebra symmetry by Thomas Creutzig, Naoki Genra, Yasuaki Hikida, Tianshu Liu

“…W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra g and an sl(2)-embedding into g. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. …”
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Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings by Riccardo Borsato, Linus Wulff

“…The latter construction is the natural generalization of the so-called Yang-Baxter deformations, based on solutions of the classical Yang-Baxter equation on the Lie algebra of G and originally constructed for group manifolds and (super)coset sigma models. …”
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Relative Pose Estimation Based on Pairwise Range With Application to Aerobridge by Ruican Xia, Hailong Pei

“…This article proposes a promising framework using pairwise range to estimate the relative pose parameterized with Lie algebra. It is compatible with the existing Gauss-Newton method and the Levenberg-Marquardt method. …”
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Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physic... by Adeyemo Oke Davies, Khalique Chaudry Masood

“…Additionally, we construct various commutations along Lie-adjoint representation tables connected to the nine-dimensional Lie algebra achieved. Further to that, detailed and comprehensive computation of the optimal system of one-dimensional subalgebras linked to the algebra is also unveiled for the under-investigated model. …”
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Gray matter changes in subjects at high risk for developing psychosis and first-episode schizophrenia: a voxel-based structural MRI study by Kazue eNakamura, Tsutomu eTakahashi, Tsutomu eTakahashi, Kiyotaka eNemoto, Atsushi eFuruichi, Shimako eNishiyama, Yumiko eNakamura, Eiji eIkeda, Mikio eKido, Kyo eNoguchi, Hikaru eSeto, Michio eSuzuki, Michio eSuzuki

“…We used voxel-based morphometry (VBM) with the Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) tools to investigate the whole-brain difference in gray matter volume among the three groups. …”
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Geometry of pseudodifferential algebra bundles and Fourier integral operators by Mathai, Varghese, Melrose, Richard B

“…We define a natural class of connections and B-fields on the principal bundle to which Ψ ℤ is associated and obtain a de Rham representative of the Dixmier-Douady class in terms of the outer derivation on the Lie algebra and the residue trace of Guillemin and Wodzicki. …”
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Translation principle for Dirac index by Mehdi, Salah, Pandzic, Pavle, Vogan, David A

“…Let G be a finite cover of a closed connected transpose-stable subgroup of GL(n,R) with complexified Lie algebra g. Let K be a maximal compact subgroup of G, and assume that G and K have equal rank. …”
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On quantum Poisson-Lie T-duality of WZNW models by Yuho Sakatani, Yuji Satoh

“…In a concrete example of the SU(2) WZNW model, we find that the self-duality is represented as a chiral automorphism of the su ̂ $$ \hat{\mathfrak{su}} $$ (2) affine Lie algebra, though the transformation of the currents is non-local and non-linear. …”
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The solution of equations of ideal gas that describes Galileo invariant motion with helical level lines, with the collapse in the helix by Yulmukhametova, Yuliya Valer'evna

“…We consider the equations of ideal gas dynamics in a cylindrical coordinate system with the arbitrary equation of state and one two-dimensional subalgebra from the optimum system of an 11-dimensional Lie algebra of differentiation operators of the first order. …”
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On a DGL-map between derivations of Sullivan minimal models by Toshihiro Yamaguchi

“…Its DGL (differential graded Lie algebra)-model is given by the derivations $$\mathrm{Der}M(X)$$ Der M ( X ) of the Sullivan minimal model M(X) of X. …”
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Here comes the SU(N): multivariate quantum gates and gradients by Roeland Wiersema, Dylan Lewis, David Wierichs, Juan Carrasquilla, Nathan Killoran

“…In addition, we provide a theorem for the computational complexity of calculating these gradients by using results from Lie algebra theory. In doing so, we further generalize previous parameter-shift methods. …”
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GRADED UNIPOTENT GROUPS AND GROSSHANS THEORY by GERGELY BÉRCZI, FRANCES KIRWAN

“…Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. …”
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Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions by Da-Chuan Lu

“…In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space G/K, where $G$ is the UV symmetry and $K$ is generated by ${\mathfrak k}={\mathfrak h}_1\cap {\mathfrak h}_2$, and ${\mathfrak h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. …”
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[rho]-compact groups as framed manifolds by Bauer, Tilman, 1973-

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Deformation Quantization and Superconformal Symmetry in Three Dimensions by Beem, C, Peelaers, W, Rastelli, L

“…We consider examples of theories for which the moduli space of vacua is either the minimal nilpotent orbit of a simple Lie algebra or a Kleinian singularity. For minimal nilpotent orbits, the quantum algebras (and their preferred bases) can be uniquely determined. …”

Localization for quantum groups at a root of unity by Backelin, E, Kremnizer, K

“…In the paper \cite{BMR} similar results were obtained for a Lie algebra $\g_p$ in char $p$. Hence, representations of $\g_p$ and of $U_q$ (when $q$ is a p'th root of unity) are related via the cotangent bundles $T^\star X$ in char 0 and in char $p$, respectively.…”

Gamma-invariant ideals in Iwasawa algebras by Ardakov, K, Wadsley, S

“…The minimal codimension of these subspaces gives a lower bound on the homological height of I in terms of the action of a certain Lie algebra on G/G^p. If we take Gamma to be G acting on itself by conjugation, then Gamma-invariant right ideals of kG are precisely the two-sided ideals of kG, and we obtain a non-trivial lower bound on the homological height of a possible non-zero two-sided ideal. …”

Graded unipotent groups and Grosshans theory by Berczi, G, Kirwan, F

“…Let U be a unipotent group which is graded in the sense that it has an extension H by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of U are strictly positive. We study embeddings of H in a general linear group G which possess Grosshans-like properties. …”

Nonlinear Dynamics of a Cavity Containing a Two-Mode Coherent Field Interacting with Two-Level Atomic Systems by E. M. Khalil, Hashim M. Alshehri, A.-B. A. Mohamed, S. Abdel-Khalek, A.-S. F. Obada

“…Using special unitary su<inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> Lie algebra, the general solution of an intrinsic noise model is obtained when an EMF is initially in a generalized coherent state. …”
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