Non-relativistic three-dimensional supergravity theories and semigroup expansion method by Patrick Concha, Marcelo Ipinza, Lucrezia Ravera, Evelyn Rodríguez

“…To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. …”
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A method based on visual saliency for vehicle-mounted monocular camera ego-motion estimation and vehicle scale estimation by Mingxin AI, Tie LIU, Jing WANG, Jiali DING, Zejian YUAN, Yuanyuan SHANG

“…A method based on visual saliency for ego-motion estimation and scale estimation of the vehicle in front was proposed.Firstly, for the ego-motion estimation of vehicle-mounted camera, the visual saliency calculation method was used to detect and remove moving objects in the monocular image sequence containing noise.While considering the image texture and smooth region, the weighted saliency map was used to retain useful feature points, to improve the robustness of ego-motion estimation.Secondly, the distance of the vehicle in front was converted into a vehicle scale estimation, by integrating descriptor match and the strength of regularization match of the lie algebra to minimize loss function.The visual attention mechanism was used to get texture image block without shade, and the pixel in the image block weight to mitigate the effects of destroyed by noise pixel, so as to realize the robust and accurate scale estimation.Finally, several challenging datasets were used to analyze and verify the proposed method.The results show that the monocular camera ego-motion estimation method reaches the level of the stereo camera-based method, and the vehicle scale estimation method ensures the prediction accuracy while giving full play to the advantages of strong robustness.…”
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Whole brain volume changes and its correlation with clinical symptom severity in patients with schizophrenia: A DARTEL-based VBM study. by Gwang-Won Kim, Yun-Hyeon Kim, Gwang-Woo Jeong

“…Magnetic resonance image data were processed using SPM8 software with diffeomorphic anatomical registration via an exponentiated Lie algebra (DARTEL) algorithm. Patients with schizophrenia exhibited significantly decreased GM volumes of the insula, superior temporal gyrus (STG), gyrus rectus, and anterior cingulate cortex (ACC) compared with healthy controls. …”
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Twistors, the ASD Yang-Mills equations and 4d Chern-Simons theory by Roland Bittleston, David Skinner

“…Examples include a 4d analogue of the Wess-Zumino-Witten model and a theory of a Lie algebra valued scalar with a cubic two derivative interaction. …”
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SYMMETRIES AND LAX INTEGRABILITY OF THE GENERALIZED PROUDMAN-JOHNSON EQUATION by O. I. Morozov

“…In particular, if <р is a characteristic of a symmetry for a PDE Н = О then the <р-invariant solution of the PDE is a solution to the compatible over-determined system Н = О, < р = О. We show that the Lie algebra of local symmetries for the generalized Proudman-Johnson equation is infinite-dimensional. …”
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Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra by Martin Cederwall, Jakob Palmkvist

“…We apply it to cases where a grey node is added to the Dynkin diagram of a rank r + 1 Kac-Moody algebra g $$ \mathfrak{g} $$ +, which in turn is an extension of a rank r finite-dimensional semisimple simply laced Lie algebra g $$ \mathfrak{g} $$ . The algebras are specified by g $$ \mathfrak{g} $$ together with a dominant integral weight λ. …”
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Self-duality from twisted cohomology by Claude Duhr, Franziska Porkert, Cathrin Semper, Sven F. Stawinski

“…Furthermore, we show that one can associate quite generically a Lie algebra representation to an ε-factorised system. …”
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Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces by S. James Gates, Yangrui Hu, S.-N. Hazel Mak

“…These are made possible by a discovery of the dependence of the superfield component expansion on the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). …”
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Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking by Jerzy Lukierski, Stjepan Meljanac, Salvatore Mignemi, Anna Pachoł

“…In such models, with algebraic basis spanned by oˆ(D,1) Lie algebra generators, we relate the vacuum expectation values (VEV) of the spontaneously broken generators with the Abelian set of ten (Snyder, D=4) or fifteen (Yang, D=5) antisymmetric tensorial generalized coordinates, which are also used as zero order input for obtaining the perturbative solutions of quantum extended Snyder and Yang models. …”
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Superuniversality of Superdiffusion by Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

“…This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it “superuniversal.” …”
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Lie symmetry analysis for generalized short pulse equation by Zhao Weidong, Munir Muhammad Mobeen, Bashir Hajra, Ahmad Daud, Athar Muhammad

“…Then we will construct the optimal system for the Lie algebra and invariant solutions (called similarity solutions) from Lie subalgebras of generalized SPE.…”
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The group structure of dynamical transformations between quantum reference frames by Angel Ballesteros, Flaminia Giacomini, Giulia Gubitosi

“…In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. …”
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Four-Dimensional Spin Foam Perturbation Theory by João Faria Martins, Aleksandar Mikovic

“…We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group U_q(g) where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. …”
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Toric Actions on b-Symplectic Manifolds by Guillemin, Victor W, Miranda, Eva, Pires, Ana Rita, Scott, Geoffrey

“…In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus.…”
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Structure of classical (finite and affine) W-algebras by De Sole, Alberto, Kac, Victor, Valeri, Daniele

“…First, we derive an explicit formula for the Poisson bracket of the classical finite W- Algebra W[superscript fin] (g, f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f . On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W- Algebra W(g, f). …”
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On the classification of non-equal rank affine conformal embeddings and applications by Adamović, Dražen, Kac, Victor G, Frajria, Pierluigi Möseneder, Papi, Paolo, Perše, Ozren

“…We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g. …”
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New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories by Kannan, Arun S.

“…Each exceptional Lie superalgebra we construct is realized as the image of an exceptional Lie algebra equipped with a nilpotent derivation of order at most p under the semisimplification functor from Repαp to Verp.…”
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The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups by Bernhardt, Karen, 1977-

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The Small Quantum Group as a Quantum Double by Etingof, Pavel I., Gelaki, Shlomo

“…J. 5 (2) (2005) 371–378] to a simple complex Lie algebra g and a primitive root of unity q of order n2 is equivalent to Lusztig’s small quantum group uq(g) (under some conditions on n). …”
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Classification of simple linearly compact n-Lie superalgebras by Cantarini, Nicoletta, Kac, Victor

“…The list consists of four examples, one of them being the n + 1-dimensional vector product n-Lie algebra, and the remaining three infinite-dimensional n-Lie algebras.…”
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