Holonomic modules and 1-generation in the Jacobian Conjecture by Bavula, Volodymyr V.

“…Each Jacobian map $\sigma $ is extended to an endomorphism $\sigma $ of the Weyl algebra $A_n$.The Jacobian Conjecture (JC) says that every Jacobian map is an automorphism. Clearly, the Jacobian Conjecture is true iff the twisted (by $\sigma $) $P_n$-module ${}^{\sigma } P_n$ is cyclic for all Jacobian maps $\sigma $. …”
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Centralizer on Lie-ideal of Semi-prime Inverse Semi-ring by Ali JA. Abass, Mohammed Yasin, Shrooq Bahjat Smeein, Abdulahman H. Majeed

“…We extending the results of Shafiq, Aslam, Javed to α- centralizer of Inverse semiring. since R is left (right) Jordan α-centralizer on”V, we get the output R is a left (right) α-centralizer on V.”If it where α is an automorphism of V,R(u) ∈ V, for any u ∈ V, and α(Z(V))= Z(V). …”
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Subrings of I-rings and S-rings by Mamadou Sanghare

“…(S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M. It is well known that every Artinian (resp. …”
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Mixed Jacobi-like forms of several variables by Min Ho Lee

“…We study mixed Jacobi-like forms of several variables associated to equivariant maps of the Poincaré upper half-plane in connection with usual Jacobi-like forms, Hilbert modular forms, and mixed automorphic forms. We also construct a lifting of a mixed automorphic form to such a mixed Jacobi-like form.…”
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1-Quasiconformal Mappings and CR Mappings on Goursat Groups by Qing Yan Wu, Zun Wei Fu

“…This can reduce the determination of 1-quasiconformal mappings to the determination of CR automorphisms of CR manifolds, which is a fundamental problem in the theory of several complex variables.…”
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The Natural Filtration of Finite Dimensional Modular Lie Superalgebras of Special Type by Keli Zheng, Yongzheng Zhang

“…Then we prove that the natural filtration of S(n,m) is invariant under its automorphisms.…”
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Univalent Logharmonic Mappings in the Plane by Zayid Abdulhadi, Rosihan M. Ali

“…Topics discussed include mapping theorems, logharmonic automorphisms, univalent logharmonic extensions onto the unit disc or the annulus, univalent logharmonic exterior mappings, and univalent logharmonic ring mappings. …”
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Infinite-Dimensional Modular Lie Superalgebra Ω by Xiaoning Xu, Bing Mu

“…The natural filtration of the Lie superalgebra Ω is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. …”
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Discrete Weighted Pseudo-Almost Automorphy and Applications by Zhinan Xia

“…As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. …”
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On equivariant bundles and their moduli spaces by Damiolini, Chiara

“…Let $G$ be an algebraic group and $\Gamma $ a finite subgroup of automorphisms of $G$. Fix also a possibly ramified $\Gamma $-covering $\widetilde{X} \rightarrow X$. …”
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SL 2(ℝ) symmetries of SymTFT and non-invertible U(1) symmetries of Maxwell theory by Azeem Hasan, Shani Meynet, Daniele Migliorati

“…We describe how to realize these automorphisms of the SymTFT in terms of its operators and we describe their effects on the dynamical theory and its global variants. …”
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Real structures on primary Hopf surfaces by Khaled Zahraa

“…The first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces (H,s)\left(H,s), and, for any such pair, to describe in detail the following naturally associated objects : the group Auth(H,s){{\rm{Aut}}}_{h}\left(H,s) of Real automorphisms, the Real Picard group (Pic(H),sˆ*)\left({\rm{Pic}}\left(H),{\hat{s}}^{* }), and the Picard group of Real holomorphic line bundles PicR(H){{\rm{Pic}}}_{{\mathbb{R}}}\left(H). …”
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Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation by M. Eshaghi Gordji, M. B. Ghaemi, G. H. Kim, Badrkhan Alizadeh

“…Let 𝐴 be an algebra, and let 𝜃, 𝜙 be ring automorphisms of 𝐴. An additive mapping 𝐻∶𝐴→𝐴 is called a (𝜃,𝜙)-derivation if 𝐻(𝑥𝑦)=𝐻(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. …”
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Groups of Negations on the Unit Square by Jiachao Wu

“…It is proven that all the automorphisms on it form a group; the set, containing the monotonic isomorphisms and the strict negations of the first (or the second or the third) kind, with the operator “composition,” is a group G2 (or G3 or G4, correspondingly). …”
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A Quantization Procedure of Fields Based on Geometric Langlands Correspondence by Do Ngoc Diep

“…And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groups G.…”
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Geometrical Applications of Split Octonions by Merab Gogberashvili, Otari Sakhelashvili

“…This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. …”
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Doubling constructions and tensor product L-functions: coverings of the symplectic group by Eyal Kaplan

“…In this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $\operatorname {\mathrm {Sp}}_{2n}$ and $\tau $ of a certain covering group of $\operatorname {\mathrm {GL}}_k$ , with arbitrary m, n and k. …”
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Notes on (α,β)-derivations by Neşet Aydin

“…Let R be a prime ring of characteristic not 2, U a nonzero ideal of R and 0≠da(α,β)-derivation of R where α and β are automorphisms of R. i) [d(U),a]=0 then a∈Z ii) For a,b∈R, the following conditions are equivalent (I) α(a)d(x)=d(x)β(b), for all x∈U (II) Either α(a)=β(b)∈CR(d(U)) or CR(a)=CR(b)=R′ and a[a,x]=[a,x]b (or a[b,x]=[b,x]b) for all x∈U. …”
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Wreathing, discrete gauging, and non-invertible symmetries by Julius F. Grimminger, William Harding, Noppadol Mekareeya

“…We examine each subgroup G, up to automorphisms, of the permutation group S 4 that acts on the four legs of the affine D 4 quiver diagram, which is mirror dual to the 3d N $$ \mathcal{N} $$ = 4 SU(2) gauge theory with four flavours. …”
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From homogeneous metric spaces to Lie groups by Cowling, Michael G., Kivioja, Ville, Le Donne, Enrico, Nicolussi Golo, Sebastiano, Ottazzi, Alessandro

“…We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively.After a review of a number of classical results, we use the Gleason–Iwasawa–Montgomery–Yamabe–Zippin structure theory to show that for all positive $ \epsilon $, each such space is $ (1,\epsilon ) $-quasi-isometric to a connected metric Lie group (metrized with a left-invariant distance that is not necessarily Riemannian).Next, we develop the structure theory of Lie groups to show that every homogeneous metric manifold is homeomorphically roughly isometric to a quotient space of a connected amenable Lie group, and roughly isometric to a simply connected solvable metric Lie group.Third, we investigate solvable metric Lie groups in more detail, and expound on and extend work of Gordon and Wilson [31, 32] and Jablonski [44] on these, showing, for instance, that connected solvable Lie groups may be made isometric if and only if they have the same real-shadow.Finally, we show that homogeneous metric spaces that admit a metric dilation are all metric Lie groups with an automorphic dilation.…”
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