Pub Date : 2025-12-01Epub Date: 2025-10-31DOI: 10.1016/j.geomphys.2025.105691
Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz
We characterize Siklos space-times which satisfy the quasi-Einstein equation, both in the gradient and the non-gradient cases. Then, we prove that several homogeneous Siklos space-times are quasi-Einstein, and finally we provide a classification of locally conformally flat quasi-Einstein Siklos space-times.
{"title":"Quasi-Einstein Siklos space-times","authors":"Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz","doi":"10.1016/j.geomphys.2025.105691","DOIUrl":"10.1016/j.geomphys.2025.105691","url":null,"abstract":"<div><div>We characterize Siklos space-times which satisfy the quasi-Einstein equation, both in the gradient and the non-gradient cases. Then, we prove that several homogeneous Siklos space-times are quasi-Einstein, and finally we provide a classification of locally conformally flat quasi-Einstein Siklos space-times.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105691"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466559","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 : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub Date: 2025-10-22DOI: 10.1016/j.geomphys.2025.105681
Miguel Manzano , Argam Ohanyan , Roland Steinbauer
The cut-and-paste method is a procedure for constructing null thin shells by matching two regions of the same spacetime across a null hypersurface. Originally proposed by Penrose, it has so far allowed to describe purely gravitational and null-dust shells in constant-curvature backgrounds. In this paper, we extend the cut-and-paste method to null shells with arbitrary gravitational/matter content. To that aim, we first derive a locally Lipschitz continuous form of the metric of the spacetime resulting from the most general matching of two constant-curvature spacetimes with totally geodesic null boundaries, and then obtain the coordinate transformation that turns this metric into the cut-and-paste form with a Dirac-delta term. The paper includes an example of a null shell with non-trivial energy density, energy flux and pressure in Minkowski space.
{"title":"Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux","authors":"Miguel Manzano , Argam Ohanyan , Roland Steinbauer","doi":"10.1016/j.geomphys.2025.105681","DOIUrl":"10.1016/j.geomphys.2025.105681","url":null,"abstract":"<div><div>The cut-and-paste method is a procedure for constructing null thin shells by matching two regions of the same spacetime across a null hypersurface. Originally proposed by Penrose, it has so far allowed to describe purely gravitational and null-dust shells in constant-curvature backgrounds. In this paper, we extend the cut-and-paste method to null shells with arbitrary gravitational/matter content. To that aim, we first derive a locally Lipschitz continuous form of the metric of the spacetime resulting from the most general matching of two constant-curvature spacetimes with totally geodesic null boundaries, and then obtain the coordinate transformation that turns this metric into the cut-and-paste form with a Dirac-delta term. The paper includes an example of a null shell with non-trivial energy density, energy flux and pressure in Minkowski space.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105681"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363229","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 : 2025-12-01Epub Date: 2025-09-29DOI: 10.1016/j.geomphys.2025.105666
Stephanie Chen
The Grothendieck classes of melonic graphs satisfy a recursive relation and may be written as polynomials in the class of the moduli space with nonnegative integer coefficients, conjectured to be log-concave. In this article, we investigate log-concavity and ultra-log-concavity for the Grothendieck class of banana graphs and the three families of polynomials involved in the recursive relation. We prove that all four are log-concave, establishing the specific case of banana graphs for the log-concavity conjecture. We additionally introduce the infinite family of clasped necklaces, melonic graphs obtained by replacing an edge of a 2-banana with a string of m-bananas. Using the recursive relation, we explicitly compute the classes of clasped necklaces and prove that they too are log-concave.
{"title":"Log-concavity of the Grothendieck classes of banana graphs and clasped necklaces","authors":"Stephanie Chen","doi":"10.1016/j.geomphys.2025.105666","DOIUrl":"10.1016/j.geomphys.2025.105666","url":null,"abstract":"<div><div>The Grothendieck classes of melonic graphs satisfy a recursive relation and may be written as polynomials in the class of the moduli space <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>0</mn><mo>,</mo><mn>4</mn></mrow></msub></math></span> with nonnegative integer coefficients, conjectured to be log-concave. In this article, we investigate log-concavity and ultra-log-concavity for the Grothendieck class of banana graphs and the three families of polynomials involved in the recursive relation. We prove that all four are log-concave, establishing the specific case of banana graphs for the log-concavity conjecture. We additionally introduce the infinite family of clasped necklaces, melonic graphs obtained by replacing an edge of a 2-banana with a string of <em>m</em>-bananas. Using the recursive relation, we explicitly compute the classes of clasped necklaces and prove that they too are log-concave.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105666"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269916","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 : 2025-12-01Epub Date: 2025-09-24DOI: 10.1016/j.geomphys.2025.105652
Xiaomin Tang, Pengliang Xu
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.
{"title":"Post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations for the Heisenberg-Virasoro algebra","authors":"Xiaomin Tang, 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":"2025-12-01","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}
Pub Date : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub Date: 2025-10-22DOI: 10.1016/j.geomphys.2025.105683
Nanyan Xu, Yunhe Sheng
In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a solution of the Zamolodchikov Tetrahedron equation. We show that a central Leibniz 2-algebra gives rise to a linear 2-rack if the underlying 2-vector space is splittable. Finally we discuss the relation between linear 2-racks and 2-racks, and show that a linear 2-rack gives rise to a 2-rack structure on the group-like category. A concrete example of strict 2-racks is constructed from an action of a strict 2-group.
{"title":"Leibniz 2-algebras, linear 2-racks and the Zamolodchikov Tetrahedron equation","authors":"Nanyan Xu, Yunhe Sheng","doi":"10.1016/j.geomphys.2025.105683","DOIUrl":"10.1016/j.geomphys.2025.105683","url":null,"abstract":"<div><div>In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a solution of the Zamolodchikov Tetrahedron equation. We show that a central Leibniz 2-algebra gives rise to a linear 2-rack if the underlying 2-vector space is splittable. Finally we discuss the relation between linear 2-racks and 2-racks, and show that a linear 2-rack gives rise to a 2-rack structure on the group-like category. A concrete example of strict 2-racks is constructed from an action of a strict 2-group.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105683"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417176","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 : 2025-12-01Epub Date: 2025-10-27DOI: 10.1016/j.geomphys.2025.105689
Yu.B. Chernyakov , G.I. Sharygin
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real symmetric matrices) and the vector fields on the group of orthogonal matrices: it is known that this system is equivalent to an ordinary differential equation on the orthogonal group, and we extend this observation further to its first integrals. As a by-product we describe a representation of the Lie algebra of -invariant functions on the dual space of Lie algebra (under the canonical Poisson structure) by vector fields on .
{"title":"Full symmetric Toda system and vector fields on the group SOn(R)","authors":"Yu.B. Chernyakov , G.I. Sharygin","doi":"10.1016/j.geomphys.2025.105689","DOIUrl":"10.1016/j.geomphys.2025.105689","url":null,"abstract":"<div><div>In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real symmetric matrices) and the vector fields on the group of orthogonal matrices: it is known that this system is equivalent to an ordinary differential equation on the orthogonal group, and we extend this observation further to its first integrals. As a by-product we describe a representation of the Lie algebra of <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>-invariant functions on the dual space of Lie algebra <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> (under the canonical Poisson structure) by vector fields on <span><math><mi>S</mi><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105689"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417178","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 : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub 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":"2025-12-01","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}
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