Pub Date : 2025-10-16DOI: 10.1016/j.geomphys.2025.105680
Shilin Ma , Yixuan Ouyang , Yemo Wu , Dafeng Zuo
We show the existence of Frobenius structures on the orbit space of the symmetric group and construct Landau–Ginzburg superpotentials for these Dubrovin-Frobenius manifolds.
{"title":"Dubrovin-Frobenius manifold structures on the orbit space of the symmetric group-III","authors":"Shilin Ma , Yixuan Ouyang , Yemo Wu , Dafeng Zuo","doi":"10.1016/j.geomphys.2025.105680","DOIUrl":"10.1016/j.geomphys.2025.105680","url":null,"abstract":"<div><div>We show the existence of Frobenius structures on the orbit space of the symmetric group and construct Landau–Ginzburg superpotentials for these Dubrovin-Frobenius manifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105680"},"PeriodicalIF":1.2,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417175","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}
Pub Date : 2025-10-13DOI: 10.1016/j.geomphys.2025.105678
Chandan Das, Himadri Shekhar Mondal
In this article, we show that if M is a globally hyperbolic spacetime with a non-compact Cauchy hypersurface Σ, then the future (past) admissible system endowed with the Vietoris topology is simply connected. The natural map between the causal future (past) of Σ, and the future (past) admissible system is continuous and bijective. But through a counter example, we show that the maps need not be homeomorphisms.
{"title":"Causally admissible system and the topology of a globally hyperbolic spacetime with non-compact Cauchy surfaces","authors":"Chandan Das, Himadri Shekhar Mondal","doi":"10.1016/j.geomphys.2025.105678","DOIUrl":"10.1016/j.geomphys.2025.105678","url":null,"abstract":"<div><div>In this article, we show that if <em>M</em> is a globally hyperbolic spacetime with a non-compact Cauchy hypersurface Σ, then the future (past) admissible system <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> <span><math><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span> endowed with the Vietoris topology is simply connected. The natural map <span><math><mi>p</mi><mo>↦</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> <span><math><mo>(</mo><mi>p</mi><mo>↦</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></math></span> between the causal future (past) of Σ, <span><math><msup><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mi>Σ</mi><mo>)</mo></math></span> <span><math><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>Σ</mi><mo>)</mo><mo>)</mo></math></span> and the future (past) admissible system <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> <span><math><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span> is continuous and bijective. But through a counter example, we show that the maps need not be homeomorphisms.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105678"},"PeriodicalIF":1.2,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363228","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}
Pub Date : 2025-10-10DOI: 10.1016/j.geomphys.2025.105674
Alexander Polishchuk
We study the standard family of supercurves of genus 1 with underlying odd spin structures. We give a simple algebraic description of this family and of the compactified family of stable supercurves with one Neveu-Schwarz puncture. We also describe the Gauss-Manin connection on the 1st de Rham cohomology of this family, and compute the superperiods of global differentials.
研究了具有奇自旋结构的1属超曲线标准族。我们给出了这个族和具有一个Neveu-Schwarz穿孔的紧化稳定超曲线族的简单代数描述。我们还描述了这个族的第1 de Rham上同调上的gaas - manin连接，并计算了全局微分的超周期。
{"title":"On supercurves of genus 1 with an underlying odd spin structure","authors":"Alexander Polishchuk","doi":"10.1016/j.geomphys.2025.105674","DOIUrl":"10.1016/j.geomphys.2025.105674","url":null,"abstract":"<div><div>We study the standard family of supercurves of genus 1 with underlying odd spin structures. We give a simple algebraic description of this family and of the compactified family of stable supercurves with one Neveu-Schwarz puncture. We also describe the Gauss-Manin connection on the 1st de Rham cohomology of this family, and compute the superperiods of global differentials.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105674"},"PeriodicalIF":1.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321866","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}
Pub Date : 2025-10-10DOI: 10.1016/j.geomphys.2025.105675
Nan Gao , Yu-Xiao Yang , Chi-Heng Zhang
Two classes of well-known algebraic triangulated categories on finite dimensional Lie superalgebra over a complex field are studied. One is the stable category of -graded Gorenstein projective -modules, and the other is the derived category of -graded -modules, where model structure and separable monad are taken as crucial tools. Model structure and Gorensteinness are also provided with the good module categories, introduced by Coulembier [7] because of Frobenius extension. At last, a specific example of good module category is applied.
{"title":"Algebraic triangulated category over Lie superalgebras","authors":"Nan Gao , Yu-Xiao Yang , Chi-Heng Zhang","doi":"10.1016/j.geomphys.2025.105675","DOIUrl":"10.1016/j.geomphys.2025.105675","url":null,"abstract":"<div><div>Two classes of well-known algebraic triangulated categories on finite dimensional Lie superalgebra <span><math><mi>g</mi></math></span> over a complex field are studied. One is the stable category of <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-graded Gorenstein projective <span><math><mi>g</mi></math></span>-modules, and the other is the derived category of <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-graded <span><math><mi>g</mi></math></span>-modules, where model structure and separable monad are taken as crucial tools. Model structure and Gorensteinness are also provided with the good module categories, introduced by Coulembier <span><span>[7]</span></span> because of Frobenius extension. At last, a specific example of good module category is applied.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105675"},"PeriodicalIF":1.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321864","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}
Pub Date : 2025-10-09DOI: 10.1016/j.geomphys.2025.105669
Jørgen Ellegaard Andersen , William Elbæk Mistegård
Let be the one-dimensional complex torus. We consider the action of an automorphism f of a Riemann surface X on the cohomology of the -equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index . We prove a formula for it in terms of cohomological pairings of canonical -equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface .
设T为一维复环面。考虑了一个Riemann曲面X的自同构f对X上具有奇次固定行列式的二阶希格斯束的模空间M上的t等变行列式线束L的上同调的作用。定义并研究了自同构等变Hitchin指数χT（M，L,f）。利用商黎曼曲面X/ < f >上抛物希格斯束模空间的正则t等变类的上同调对证明了它的一个公式。
{"title":"The automorphism equivariant Hitchin index","authors":"Jørgen Ellegaard Andersen , William Elbæk Mistegård","doi":"10.1016/j.geomphys.2025.105669","DOIUrl":"10.1016/j.geomphys.2025.105669","url":null,"abstract":"<div><div>Let <span><math><mi>T</mi></math></span> be the one-dimensional complex torus. We consider the action of an automorphism <em>f</em> of a Riemann surface <em>X</em> on the cohomology of the <span><math><mi>T</mi></math></span>-equivariant determinant line bundle <span><math><mi>L</mi></math></span> over the moduli space <span><math><mi>M</mi></math></span> of rank two Higgs bundles on <em>X</em> with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>M</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span>. We prove a formula for it in terms of cohomological pairings of canonical <span><math><mi>T</mi></math></span>-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface <span><math><mi>X</mi><mo>/</mo><mo>〈</mo><mi>f</mi><mo>〉</mo></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105669"},"PeriodicalIF":1.2,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417182","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}
Pub Date : 2025-10-08DOI: 10.1016/j.geomphys.2025.105677
S. Braiek , T. Chtioui , M. Elhamdadi , S. Mabrouk
We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two characterizations of relative averaging operators of Hom-associative algebras via graphs and Nijenhuis operators. A (homomorphic) relative averaging operator of Hom-associative algebras with respect to a given representation gives rise to Hom-associative (tri)dialgebras. By admissibility, a Hom-Jordan (tri)dialgebra and a Hom-(tri)Leibniz algebra can be obtained from Hom-associative (tri)dialgebra.
{"title":"Hom-associative algebras, admissibility and relative averaging operators","authors":"S. Braiek , T. Chtioui , M. Elhamdadi , S. Mabrouk","doi":"10.1016/j.geomphys.2025.105677","DOIUrl":"10.1016/j.geomphys.2025.105677","url":null,"abstract":"<div><div>We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two characterizations of relative averaging operators of Hom-associative algebras via graphs and Nijenhuis operators. A (homomorphic) relative averaging operator of Hom-associative algebras with respect to a given representation gives rise to Hom-associative (tri)dialgebras. By admissibility, a Hom-Jordan (tri)dialgebra and a Hom-(tri)Leibniz algebra can be obtained from Hom-associative (tri)dialgebra.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105677"},"PeriodicalIF":1.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321865","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}
Pub Date : 2025-10-08DOI: 10.1016/j.geomphys.2025.105673
Bruce Lionnel Lietap Ndi , Djagwa Dehainsala , Joseph Dongho
The aim of this work is focused on the linearization and the determination of a Lax representation for the algebraic complete integrability (a.c.i.) Toda lattice associated with the twisted affine Lie algebra . Firstly, we recall that our case of a.c.i. is a two-dimensional algebraic completely integrable systems for which the invariant (real) tori can be extended to complex algebraic tori (abelian surfaces). Secondly, we show that the lattice is related to the Mumford system and we construct an explicit morphism between these systems. Finally, we give a Lax equation for this Toda lattice and we construct an explicit linearization of the system.
{"title":"Linearization, separability and Lax representation for the a4(2) twisted affine Lie Toda lattice","authors":"Bruce Lionnel Lietap Ndi , Djagwa Dehainsala , Joseph Dongho","doi":"10.1016/j.geomphys.2025.105673","DOIUrl":"10.1016/j.geomphys.2025.105673","url":null,"abstract":"<div><div>The aim of this work is focused on the linearization and the determination of a Lax representation for the algebraic complete integrability (a.c.i.) Toda lattice associated with the twisted affine Lie algebra <span><math><msubsup><mrow><mi>a</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span>. Firstly, we recall that our case of a.c.i. is a two-dimensional algebraic completely integrable systems for which the invariant (real) tori can be extended to complex algebraic tori (abelian surfaces). Secondly, we show that the lattice is related to the Mumford system and we construct an explicit morphism between these systems. Finally, we give a Lax equation for this Toda lattice and we construct an explicit linearization of the system.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105673"},"PeriodicalIF":1.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321862","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}
Pub Date : 2025-10-08DOI: 10.1016/j.geomphys.2025.105672
Hengyun Yang , Yang Zhang
We construct central elements in the degenerate quantum general linear group in the sense of Cheng, Wang, and R. B. Zhang [1], and in particular, give an explicit formula for the corresponding quantum Casimir element. Our approach is based on the explicit L-operators, and we further construct a universal L-operator, which is a spectral parameter-dependent solution of the quantum Yang-Baxter equation. This in turn yields an RLL realisation of the degenerate quantum general linear group. Our main results indicate deep links with the quantum general linear supergroup, thereby providing new directions for studying its structure and representations.
本文构造了Cheng， Wang， R. B. Zhang[1]意义上的简并量子一般线性群的中心元，并给出了相应的量子卡西米尔元的显式公式。我们的方法基于显式l算子，并进一步构造了一个泛l算子，它是量子Yang-Baxter方程的谱参数相关解。这反过来又产生了简并量子一般线性群的RLL实现。我们的主要结果表明了与量子一般线性超群的深层联系，从而为研究其结构和表示提供了新的方向。
{"title":"Central elements of the degenerate quantum general linear group","authors":"Hengyun Yang , Yang Zhang","doi":"10.1016/j.geomphys.2025.105672","DOIUrl":"10.1016/j.geomphys.2025.105672","url":null,"abstract":"<div><div>We construct central elements in the degenerate quantum general linear group in the sense of Cheng, Wang, and R. B. Zhang <span><span>[1]</span></span>, and in particular, give an explicit formula for the corresponding quantum Casimir element. Our approach is based on the explicit <em>L</em>-operators, and we further construct a universal <em>L</em>-operator, which is a spectral parameter-dependent solution of the quantum Yang-Baxter equation. This in turn yields an RLL realisation of the degenerate quantum general linear group. Our main results indicate deep links with the quantum general linear supergroup, thereby providing new directions for studying its structure and representations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105672"},"PeriodicalIF":1.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321863","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}
Pub Date : 2025-10-08DOI: 10.1016/j.geomphys.2025.105676
Yi Li, Donghe Pei
In this paper, we define the equi-centro-affine position-dual and tangent-dual curves in the equi-centro-affine plane. Meanwhile, from the perspective of singularity theory of smooth functions, we establish the relationships between the singularities of position-dual and tangent-dual curves and the singularities of tangent curve, as well as the geometric invariants of plane curves. Moreover, we consider the relationships among position-dual and tangent-dual curves and other curves in the equi-centro-affine plane.
{"title":"Generic equi-centro-affine differential geometry of position-dual and tangent-dual curves","authors":"Yi Li, Donghe Pei","doi":"10.1016/j.geomphys.2025.105676","DOIUrl":"10.1016/j.geomphys.2025.105676","url":null,"abstract":"<div><div>In this paper, we define the equi-centro-affine position-dual and tangent-dual curves in the equi-centro-affine plane. Meanwhile, from the perspective of singularity theory of smooth functions, we establish the relationships between the singularities of position-dual and tangent-dual curves and the singularities of tangent curve, as well as the geometric invariants of plane curves. Moreover, we consider the relationships among position-dual and tangent-dual curves and other curves in the equi-centro-affine plane.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105676"},"PeriodicalIF":1.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321868","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}
Pub Date : 2025-10-08DOI: 10.1016/j.geomphys.2025.105671
Maria Matushko
We propose a trigonometric solution of the associative Yang-Baxter equation related to the queer Lie superalgebra which in its turn satisfies the quantum Yang-Baxter equation.
{"title":"A solution of the associative Yang-Baxter equation related to the queer Lie superalgebra","authors":"Maria Matushko","doi":"10.1016/j.geomphys.2025.105671","DOIUrl":"10.1016/j.geomphys.2025.105671","url":null,"abstract":"<div><div>We propose a trigonometric solution of the associative Yang-Baxter equation related to the queer Lie superalgebra which in its turn satisfies the quantum Yang-Baxter equation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105671"},"PeriodicalIF":1.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321869","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}
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