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Super Kupershmidt operator and the Yang-Baxter equation in Malcev superalgebras Malcev超代数中的超级Kupershmidt算子和Yang-Baxter方程
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-29 DOI: 10.1016/j.geomphys.2025.105663
Yinuo Zhao , Liangyun Chen
{"title":"Super Kupershmidt operator and the Yang-Baxter equation in Malcev superalgebras","authors":"Yinuo Zhao ,&nbsp;Liangyun Chen","doi":"10.1016/j.geomphys.2025.105663","DOIUrl":"10.1016/j.geomphys.2025.105663","url":null,"abstract":"<div><div>In this paper, we show the relationship between skew-symmetric solutions of the Yang-Baxter equation (YBE) and super Kupershmidt operators of Malcev superalgebras. First, we show that a skew-supersymmetric solution of the Yang-Baxter equation on a Malcev superalgebra can be interpreted as an super Kupershmidt operator associated to the coadjoint representation. On this basis, when considering non-degenerate skew-symmetric solutions of the Yang-Baxter equation, this connection can be enhanced with symplectic forms. We also show that super Kupershmidt operators associated with a general representation could give skew-symmetric solutions of the Yang-Baxter equation on certain semi-direct products of Malcev superalgebras. What's more, we reveal that in the case of pre-Malcev superalgebras, We can get similar results between the Yang-Baxter equation and super Kupershmidt operators.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105663"},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Connections and Higgs bundles on curves defined over a number field 数域上曲线上的连接和希格斯束
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-29 DOI: 10.1016/j.geomphys.2025.105664
Indranil Biswas , Sudarshan Gurjar
{"title":"Connections and Higgs bundles on curves defined over a number field","authors":"Indranil Biswas ,&nbsp;Sudarshan Gurjar","doi":"10.1016/j.geomphys.2025.105664","DOIUrl":"10.1016/j.geomphys.2025.105664","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> be an irreducible smooth projective curve defined over <span><math><mover><mrow><mi>Q</mi></mrow><mo>‾</mo></mover></math></span> and <span><math><mi>E</mi></math></span> a vector bundle on <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. We give a criterion for connections on the base change <span><math><mi>E</mi><msub><mrow><mo>⊗</mo></mrow><mrow><mover><mrow><mi>Q</mi></mrow><mo>‾</mo></mover></mrow></msub><mi>C</mi><mspace></mspace><mo>⟶</mo><mspace></mspace><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><msub><mrow><mo>×</mo></mrow><mrow><mrow><mi>Spec</mi></mrow><mspace></mspace><mover><mrow><mi>Q</mi></mrow><mo>‾</mo></mover></mrow></msub><mrow><mi>Spec</mi></mrow><mspace></mspace><mi>C</mi></math></span> to <span><math><mi>C</mi></math></span> to be the base change of some connection on <span><math><mi>E</mi></math></span>. A similar criterion is given for Higgs fields on <span><math><mi>E</mi><msub><mrow><mo>⊗</mo></mrow><mrow><mover><mrow><mi>Q</mi></mrow><mo>‾</mo></mover></mrow></msub><mi>C</mi></math></span></div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105664"},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations for the Heisenberg-Virasoro algebra Heisenberg-Virasoro代数的后李代数结构，Rota-Baxter算子和Yang-Baxter方程
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105652
Xiaomin Tang, Pengliang Xu
{"title":"Post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations for the Heisenberg-Virasoro algebra","authors":"Xiaomin Tang,&nbsp;Pengliang Xu","doi":"10.1016/j.geomphys.2025.105652","DOIUrl":"10.1016/j.geomphys.2025.105652","url":null,"abstract":"<div><div>In this paper, we provide a complete characterization of the graded post-Lie algebra structures on the Heisenberg-Virasoro algebra. As applications, we investigate the homogeneous Rota-Baxter operators (of weight 1) on the Heisenberg-Virasoro algebra and a class of solutions of the formal classical Yang-Baxter equation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105652"},"PeriodicalIF":1.2,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyperbolic Monge–Ampère systems with S1 = 0 具有S1 = 的双曲monge - ampantere系统
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105655
Yuhao Hu
{"title":"Hyperbolic Monge–Ampère systems with S1 = 0","authors":"Yuhao Hu","doi":"10.1016/j.geomphys.2025.105655","DOIUrl":"10.1016/j.geomphys.2025.105655","url":null,"abstract":"<div><div>For hyperbolic Monge–Ampère systems, a well-known solution of the equivalence problem yields two invariant tensors, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, defined on the underlying 5-manifold, where <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> characterizes systems that are Euler–Lagrange. In this article, we consider the ‘opposite’ case, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>, and show that the local generality of such systems is ‘2 arbitrary functions of 3 variables’. In addition, we classify all <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> systems with cohomogeneity at most one, which turn out to be linear up to contact transformations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105655"},"PeriodicalIF":1.2,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and Tempesta–Tondo conjecture 小维算子域的Jordan-Chevalley分解问题及Tempesta-Tondo猜想
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105656
Alexey V. Bolsinov , Andrey Yu. Konyaev , Vladimir S. Matveev
{"title":"On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and Tempesta–Tondo conjecture","authors":"Alexey V. Bolsinov ,&nbsp;Andrey Yu. Konyaev ,&nbsp;Vladimir S. Matveev","doi":"10.1016/j.geomphys.2025.105656","DOIUrl":"10.1016/j.geomphys.2025.105656","url":null,"abstract":"<div><div>We explore the Jordan–Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field <em>L</em>, similar to a nilpotent Jordan block, to possess local coordinates in which <em>L</em> takes a strictly upper triangular form. We prove the Tempesta–Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105656"},"PeriodicalIF":1.2,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conjugate points in the Grassmann manifold of a C⁎-algebra C -代数的Grassmann流形中的共轭点
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105654
Esteban Andruchow , Gabriel Larotonda , Lázaro Recht
{"title":"Conjugate points in the Grassmann manifold of a C⁎-algebra","authors":"Esteban Andruchow ,&nbsp;Gabriel Larotonda ,&nbsp;Lázaro Recht","doi":"10.1016/j.geomphys.2025.105654","DOIUrl":"10.1016/j.geomphys.2025.105654","url":null,"abstract":"<div><div>Let <figure><img></figure> be a component of the Grassmann manifold of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra, presented as the unitary orbit of a given orthogonal projection <figure><img></figure>. There are several natural connections on this manifold, and we first show that they all agree (in the presence of a finite trace in <span><math><mi>A</mi></math></span>, when we give <figure><img></figure> the Riemannian metric induced by the Killing form, this is the Levi-Civita connection of the metric). We study the cut locus of <figure><img></figure> for the spectral rectifiable distance, and also the conjugate tangent locus of <figure><img></figure> along a geodesic. Furthermore, for each tangent vector <em>V</em> at <em>P</em>, we compute the kernel of the differential of the exponential map of the connection. We exhibit examples where points that are tangent conjugate in the classical setting, fail to be conjugate: in some cases they are not monoconjugate but epinconjugate, and in other cases they are not conjugate at all.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105654"},"PeriodicalIF":1.2,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Differential invariants of systems of two nonlinear elliptic partial differential equations by Lie symmetry method 用李对称方法求两个非线性椭圆型偏微分方程系统的微分不变量
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-22 DOI: 10.1016/j.geomphys.2025.105650
M. Huzaifa Yaseen , Rida Hashmi , Najla A. Mohammed , Hala A Hejazi
{"title":"Differential invariants of systems of two nonlinear elliptic partial differential equations by Lie symmetry method","authors":"M. Huzaifa Yaseen ,&nbsp;Rida Hashmi ,&nbsp;Najla A. Mohammed ,&nbsp;Hala A Hejazi","doi":"10.1016/j.geomphys.2025.105650","DOIUrl":"10.1016/j.geomphys.2025.105650","url":null,"abstract":"<div><div>The Lie symmetry method offers a systematic approach for analyzing and solving differential equations by identifying continuous transformations that preserve their structure. In this study, we investigate a general system of two nonlinear second-order elliptic partial differential equations using Lie symmetry techniques. We compute the equivalence transformations for the system, which serve as the foundation for deriving differential invariants. Specifically, we establish both joint differential invariants that are obtained under transformations of dependent and independent variables along with semi-differential invariants, derived solely from transformations of dependent variables. These invariants play a crucial role in reducing the system to its simplest possible form while retaining its essential features. By applying these differential invariants, we present reduced forms of various nonlinear systems of elliptic partial differential equations, demonstrating the effectiveness of the method in simplifying complex equations. Our results highlight the utility of Lie symmetry analysis in deriving invariant structures and facilitating the systematic reduction of coupled nonlinear systems of partial differential equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105650"},"PeriodicalIF":1.2,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On generalized Poisson algebras: Solvability and constructions 广义泊松代数：可解性及其构造
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-18 DOI: 10.1016/j.geomphys.2025.105649
Xinru Cao , Zafar Normatov , Bakhrom Omirov , Jie Ruan
{"title":"On generalized Poisson algebras: Solvability and constructions","authors":"Xinru Cao ,&nbsp;Zafar Normatov ,&nbsp;Bakhrom Omirov ,&nbsp;Jie Ruan","doi":"10.1016/j.geomphys.2025.105649","DOIUrl":"10.1016/j.geomphys.2025.105649","url":null,"abstract":"<div><div>This paper investigates nilpotent and solvable structures in generalized Poisson algebras, establishing analogues of Engel's and Lie's theorems within this context. We present several constructions of generalized Poisson algebras, including those derived from null-filiform and filiform associative commutative algebras, and explore extensions through unit adjunction and generalized Wronskian Lie algebras. Using polarization techniques, we establish fundamental equivalences between algebraic structures and characterize admissible algebras. Finally, we provide a complete classification of complex nilpotent generalized Poisson algebras up to dimension three.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105649"},"PeriodicalIF":1.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the construction of generalized rectifying ruled surfaces in 3-dimensional Lie groups 三维李群中广义校正直纹曲面的构造
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-18 DOI: 10.1016/j.geomphys.2025.105651
Bahar Doğan Yazıcı
{"title":"On the construction of generalized rectifying ruled surfaces in 3-dimensional Lie groups","authors":"Bahar Doğan Yazıcı","doi":"10.1016/j.geomphys.2025.105651","DOIUrl":"10.1016/j.geomphys.2025.105651","url":null,"abstract":"<div><div>In this study, we investigate the geometry of generalized rectifying ruled surfaces in the 3-dimensional Lie group <span><math><mi>G</mi></math></span>. We construct geometric structures such as singular point sets, cylindrical surfaces, striction curves, developable surfaces, geodesic and asymptotic curves, as well as the Gauss and mean curvatures of generalized rectifying ruled surfaces in <span><math><mi>G</mi></math></span>. Then, we present the shape operator matrix and some related characterizations of developable generalized rectifying ruled surfaces in the 3-dimensional Lie group <span><math><mi>G</mi></math></span>. We also discuss how generalized rectifying ruled surfaces in 3-dimensional Lie groups correspond, in special cases, to tangent developable ruled surfaces, binormal ruled surfaces, and rectifying ruled surfaces both in 3-dimensional Lie groups and in 3-dimensional Euclidean space.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105651"},"PeriodicalIF":1.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Anisotropic Gauss curvature flow of complete non-compact graphs 完全非紧图的各向异性高斯曲率流
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-09-16 DOI: 10.1016/j.geomphys.2025.105648
Shujing Pan, Yong Wei
{"title":"Anisotropic Gauss curvature flow of complete non-compact graphs","authors":"Shujing Pan,&nbsp;Yong Wei","doi":"10.1016/j.geomphys.2025.105648","DOIUrl":"10.1016/j.geomphys.2025.105648","url":null,"abstract":"<div><div>In this paper, we consider the anisotropic <em>α</em>-Gauss curvature flow for complete noncompact convex hypersurfaces in the Euclidean space with the anisotropy determined by a smooth closed uniformly convex Wulff shape. We show that for all positive power <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span>, if the initial hypersurface is complete noncompact and locally uniformly convex, then there exists a complete, noncompact, smooth and strictly convex solution of the flow which is defined for all positive time.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105648"},"PeriodicalIF":1.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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