Pub Date : 2025-11-21DOI: 10.1016/j.geomphys.2025.105714
Khaled Basdouri , Ghaith Chaabane
Recent research has extensively explored Bihom-structures. In this paper, we introduce the notion of double Bihom–Lie superbialgebras and develop a corresponding cohomology theory, defined as the total cohomology of a double complex constructed from a Bihom–Lie superalgebra and its dual. We demonstrate that the second cohomology group classifies formal deformations of Bihom–Lie superbialgebras. Furthermore, we provide explicit computations and examples in low-dimensional cases to illustrate these results.
{"title":"Cohomology of Bihom-Lie superbialgebras","authors":"Khaled Basdouri , Ghaith Chaabane","doi":"10.1016/j.geomphys.2025.105714","DOIUrl":"10.1016/j.geomphys.2025.105714","url":null,"abstract":"<div><div>Recent research has extensively explored Bihom-structures. In this paper, we introduce the notion of double Bihom–Lie superbialgebras and develop a corresponding cohomology theory, defined as the total cohomology of a double complex constructed from a Bihom–Lie superalgebra and its dual. We demonstrate that the second cohomology group classifies formal deformations of Bihom–Lie superbialgebras. Furthermore, we provide explicit computations and examples in low-dimensional cases to illustrate these results.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105714"},"PeriodicalIF":1.2,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145697785","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 : 2025-11-20DOI: 10.1016/j.geomphys.2025.105717
Abraham Bobadilla Osses , Mauricio Godoy Molina
In this paper, we study the mechanical system associated with rolling a Lorentzian manifold of dimension on flat Lorentzian space , without slipping or twisting. Using previous results, it is known that there exists a distribution of rank defined on the configuration space of the rolling system, encoding the no-slip and no-twist conditions. Our objective is to study the problem of complete controllability of the control system associated with . The key lies in examining the holonomy group of the distribution and, following the approach of [7], establishing that the rolling problem is completely controllable if and only if the holonomy group of equals .
{"title":"Controllability of the rolling system of a Lorentzian manifold on Rn,1","authors":"Abraham Bobadilla Osses , Mauricio Godoy Molina","doi":"10.1016/j.geomphys.2025.105717","DOIUrl":"10.1016/j.geomphys.2025.105717","url":null,"abstract":"<div><div>In this paper, we study the mechanical system associated with rolling a Lorentzian manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> of dimension <span><math><mi>n</mi><mo>+</mo><mn>1</mn><mo>≥</mo><mn>2</mn></math></span> on flat Lorentzian space <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>,</mo><mn>1</mn></mrow></msup></math></span>, without slipping or twisting. Using previous results, it is known that there exists a distribution <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> of rank <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> defined on the configuration space <span><math><mi>Q</mi><mo>(</mo><mi>M</mi><mo>,</mo><mover><mrow><mi>M</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> of the rolling system, encoding the no-slip and no-twist conditions. Our objective is to study the problem of complete controllability of the control system associated with <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>. The key lies in examining the holonomy group of the distribution <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> and, following the approach of <span><span>[7]</span></span>, establishing that the rolling problem is completely controllable if and only if the holonomy group of <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> equals <span><math><mi>S</mi><msub><mrow><mi>O</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105717"},"PeriodicalIF":1.2,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624553","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 : 2025-11-20DOI: 10.1016/j.geomphys.2025.105716
Fernando A.Z. Santamaria, Elizaveta Vishnyakova
We develop the theory of H-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of H-graded coverings of supermanifolds in the case where H is a finite abelian group.
{"title":"H-covering of a supermanifold","authors":"Fernando A.Z. Santamaria, Elizaveta Vishnyakova","doi":"10.1016/j.geomphys.2025.105716","DOIUrl":"10.1016/j.geomphys.2025.105716","url":null,"abstract":"<div><div>We develop the theory of <em>H</em>-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of <em>H</em>-graded coverings of supermanifolds in the case where <em>H</em> is a finite abelian group.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105716"},"PeriodicalIF":1.2,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623713","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105713
Marc Mars , Carlos Peón-Nieto
We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector u. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the spacetime Weyl tensor with intrinsic quantities of the hypersurfaces orthogonal to u. Restricting to the case of Λ-vacuum spacetimes (with and any dimension) admiting a conformal compactification, we then study the behavior of the Weyl tensor near by means of an asymptotic expansion à la Fefferman-Graham, where the first terms are explicitly computed. We use these tools to characterize four dimensional algebraically special spacetimes with locally conformally flat , showing they match exactly the so-called Kerr-de Sitter-like class with conformally flat , thus providing a geometric characterization of this class of spacetimes.
{"title":"Classification of Λ ≠ 0-vacuum algebraically special spacetimes with conformally flat I from Weyl tensor expansion","authors":"Marc Mars , Carlos Peón-Nieto","doi":"10.1016/j.geomphys.2025.105713","DOIUrl":"10.1016/j.geomphys.2025.105713","url":null,"abstract":"<div><div>We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector <em>u</em>. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the spacetime Weyl tensor with intrinsic quantities of the hypersurfaces orthogonal to <em>u</em>. Restricting to the case of Λ-vacuum spacetimes (with <span><math><mi>Λ</mi><mo>≠</mo><mn>0</mn></math></span> and any dimension) admiting a conformal compactification, we then study the behavior of the Weyl tensor near <span><math><mi>I</mi></math></span> by means of an asymptotic expansion <em>à la</em> Fefferman-Graham, where the first terms are explicitly computed. We use these tools to characterize four dimensional algebraically special spacetimes with locally conformally flat <span><math><mi>I</mi></math></span>, showing they match exactly the so-called <em>Kerr-de Sitter-like class with conformally flat</em> <span><math><mi>I</mi></math></span>, thus providing a geometric characterization of this class of spacetimes.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105713"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624552","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105715
Donghoon Jang
To classify a group action on a manifold, the data associated with the fixed point set is essential. In this paper, we classify the fixed point data of a circle action on a 6-dimensional compact connected oriented manifold with isolated fixed points, where the fixed point data consists of the collection of signs and weights at the fixed points. We show that this fixed point data can be reduced to the empty collection by performing a sequence of operations. Specifically, we prove that one can successively take equivariant connected sums at fixed points with , , or 6-dimensional analogues of the Hirzebruch surfaces (and their oppositely oriented counterparts), resulting in a fixed-point-free action on a compact connected oriented 6-manifold.
{"title":"Circle actions on six dimensional oriented manifolds with isolated fixed points","authors":"Donghoon Jang","doi":"10.1016/j.geomphys.2025.105715","DOIUrl":"10.1016/j.geomphys.2025.105715","url":null,"abstract":"<div><div>To classify a group action on a manifold, the data associated with the fixed point set is essential. In this paper, we classify the fixed point data of a circle action on a 6-dimensional compact connected oriented manifold with isolated fixed points, where the fixed point data consists of the collection of signs and weights at the fixed points. We show that this fixed point data can be reduced to the empty collection by performing a sequence of operations. Specifically, we prove that one can successively take equivariant connected sums at fixed points with <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>CP</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, or 6-dimensional analogues of the Hirzebruch surfaces (and their oppositely oriented counterparts), resulting in a fixed-point-free action on a compact connected oriented 6-manifold.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105715"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579505","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105712
Taoufik Chtioui
In this paper, we extend the concept of anti-Leibniz algebras to the conformal setting and establish an equivalent characterization for a distinguished class of such structures, called quadratic anti-Leibniz conformal algebras. We develop the representation theory of anti-Leibniz conformal algebras and explore its structural consequences. We also introduce and study -operators on anti-Leibniz conformal algebras, which provide systematic tools for constructing new conformal algebraic structures called anti-Leibniz–dendriform conformal algebras. In addition, we investigate embedding tensors on Jacobi–Jordan conformal algebras, emphasizing their connection with anti-Leibniz conformal structures and showing how they can be used to generate new examples.
{"title":"Anti-Leibniz conformal algebras and related structures via splitting and duplication","authors":"Taoufik Chtioui","doi":"10.1016/j.geomphys.2025.105712","DOIUrl":"10.1016/j.geomphys.2025.105712","url":null,"abstract":"<div><div>In this paper, we extend the concept of anti-Leibniz algebras to the conformal setting and establish an equivalent characterization for a distinguished class of such structures, called quadratic anti-Leibniz conformal algebras. We develop the representation theory of anti-Leibniz conformal algebras and explore its structural consequences. We also introduce and study <span><math><mi>O</mi></math></span>-operators on anti-Leibniz conformal algebras, which provide systematic tools for constructing new conformal algebraic structures called anti-Leibniz–dendriform conformal algebras. In addition, we investigate embedding tensors on Jacobi–Jordan conformal algebras, emphasizing their connection with anti-Leibniz conformal structures and showing how they can be used to generate new examples.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105712"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623712","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105711
Prosenjit Mandal , Absos Ali Shaikh , Prince Majeed
This paper intends to the study of compact as well as non-compact m-Bach soliton. We have shown that a compact m-Bach soliton with either and or and is Bach flat. Later, in dimension 4 with non-zero Ricci curvature, we have manifested that a gradient m-Bach soliton is Bach flat. Again, we have determined the nature of the potential vector field on an m-Bach soliton as a conformal motion and acquired that such a motion becomes homothetic and the potential vector field is trivial. Also, in a 4-dimensional compact gradient m-Bach soliton with a condition we have established that the soliton vector field is Killing, and also deduced with an another condition that the soliton becomes steady. Furthermore, we have achieved that in a compact m-Bach soliton, the potential function differs from the Hodge-de Rham potential only by a constant. Finally, depending on the sign of m, it is demonstrated that an m-Bach soliton which is non-compact with a restriction on the potential vector field is either non-shrinking or non-expanding.
{"title":"Some results on m-Bach soliton","authors":"Prosenjit Mandal , Absos Ali Shaikh , Prince Majeed","doi":"10.1016/j.geomphys.2025.105711","DOIUrl":"10.1016/j.geomphys.2025.105711","url":null,"abstract":"<div><div>This paper intends to the study of compact as well as non-compact <em>m</em>-Bach soliton. We have shown that a compact <em>m</em>-Bach soliton with either <span><math><mi>m</mi><mo>></mo><mn>0</mn></math></span> and <span><math><mi>σ</mi><mo>≥</mo><mn>0</mn></math></span> or <span><math><mi>m</mi><mo><</mo><mn>0</mn></math></span> and <span><math><mi>σ</mi><mo>≤</mo><mn>0</mn></math></span> is Bach flat. Later, in dimension 4 with non-zero Ricci curvature, we have manifested that a gradient <em>m</em>-Bach soliton is Bach flat. Again, we have determined the nature of the potential vector field on an <em>m</em>-Bach soliton as a conformal motion and acquired that such a motion becomes homothetic and the potential vector field is trivial. Also, in a 4-dimensional compact gradient <em>m</em>-Bach soliton with a condition we have established that the soliton vector field is Killing, and also deduced with an another condition that the soliton becomes steady. Furthermore, we have achieved that in a compact <em>m</em>-Bach soliton, the potential function differs from the Hodge-de Rham potential only by a constant. Finally, depending on the sign of <em>m</em>, it is demonstrated that an <em>m</em>-Bach soliton which is non-compact with a restriction on the potential vector field is either non-shrinking or non-expanding.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105711"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579506","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105710
Ana Carolina Mançur
We verify that LA-Courant algebroids provide the Manin triple framework for double Lie bialgebroids. Specifically, we establish a correspondence between double Lie bialgebroids and LA-Manin triples, i.e., LA-Courant algebroids equipped with a pair of complementary LA-Dirac structures. As an application, LA-Courant algebroids and CA-groupoids given by Drinfeld doubles are shown to correspond via integration and differentiation.
{"title":"Manin triples for double Lie bialgebroids","authors":"Ana Carolina Mançur","doi":"10.1016/j.geomphys.2025.105710","DOIUrl":"10.1016/j.geomphys.2025.105710","url":null,"abstract":"<div><div>We verify that LA-Courant algebroids provide the Manin triple framework for double Lie bialgebroids. Specifically, we establish a correspondence between double Lie bialgebroids and LA-Manin triples, i.e., LA-Courant algebroids equipped with a pair of complementary LA-Dirac structures. As an application, LA-Courant algebroids and CA-groupoids given by Drinfeld doubles are shown to correspond via integration and differentiation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105710"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145576284","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 : 2025-11-19DOI: 10.1016/j.geomphys.2025.105718
Oleg Ogievetsky , Pavel Pyatov
For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras — special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central. In [35] we described three generating sets of the characteristic subalgebras of the symplectic and orthogonal quantum matrix algebras. One of these — the set of the elementary sums — is finite. In the symplectic case the elementary sums are in general algebraically independent. On the contrary, in the orthogonal case the elementary sums turn out to be dependent. We obtain a set of quadratic relations for these generators. We call these relations ‘reciprocal’ because they lie at the heart of the reciprocal (sometimes called palindromic) property of the characteristic polynomial of the orthogonal quantum matrices. Next, we resolve the reciprocal relations for the quantum orthogonal matrix algebra extended by the inverse of the quantum matrix. As an auxiliary result, we derive the commutation relations between the q-determinant of the quantum orthogonal matrix and the generators of the quantum matrix algebra, that is, the components of the quantum matrix.
{"title":"Reciprocal relations for orthogonal quantum matrices","authors":"Oleg Ogievetsky , Pavel Pyatov","doi":"10.1016/j.geomphys.2025.105718","DOIUrl":"10.1016/j.geomphys.2025.105718","url":null,"abstract":"<div><div>For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras — special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central. In <span><span>[35]</span></span> we described three generating sets of the characteristic subalgebras of the symplectic and orthogonal quantum matrix algebras. One of these — the set of the elementary sums — is finite. In the symplectic case the elementary sums are in general algebraically independent. On the contrary, in the orthogonal case the elementary sums turn out to be dependent. We obtain a set of quadratic relations for these generators. We call these relations ‘reciprocal’ because they lie at the heart of the reciprocal (sometimes called palindromic) property of the characteristic polynomial of the orthogonal quantum matrices. Next, we resolve the reciprocal relations for the quantum orthogonal matrix algebra extended by the inverse of the quantum matrix. As an auxiliary result, we derive the commutation relations between the <em>q</em>-determinant of the quantum orthogonal matrix and the generators of the quantum matrix algebra, that is, the components of the quantum matrix.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105718"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579509","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 : 2025-11-13DOI: 10.1016/j.geomphys.2025.105707
Weiqiang He , Yefeng Shen
We introduce Virasoro operators for any Landau-Ginzburg pair where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We propose a conjecture that the total ancestor potential of the FJRW theory of the pair is annihilated by these Virasoro operators. We prove the conjecture in various cases, including: (1) invertible polynomials with the maximal group, (2) some two-variable polynomials with the minimal group, (3) certain Calabi-Yau polynomials with groups. We also discuss the connections among Virasoro constraints, mirror symmetry of Landau-Ginzburg models, and Landau-Ginzburg/Calabi-Yau correspondence.
{"title":"Virasoro constraints in quantum singularity theories","authors":"Weiqiang He , Yefeng Shen","doi":"10.1016/j.geomphys.2025.105707","DOIUrl":"10.1016/j.geomphys.2025.105707","url":null,"abstract":"<div><div>We introduce Virasoro operators for any Landau-Ginzburg pair <span><math><mo>(</mo><mi>W</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> where <em>W</em> is a non-degenerate quasi-homogeneous polynomial and <em>G</em> is a certain group of diagonal symmetries. We propose a conjecture that the total ancestor potential of the FJRW theory of the pair <span><math><mo>(</mo><mi>W</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> is annihilated by these Virasoro operators. We prove the conjecture in various cases, including: (1) invertible polynomials with the maximal group, (2) some two-variable polynomials with the minimal group, (3) certain Calabi-Yau polynomials with groups. We also discuss the connections among Virasoro constraints, mirror symmetry of Landau-Ginzburg models, and Landau-Ginzburg/Calabi-Yau correspondence.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105707"},"PeriodicalIF":1.2,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579507","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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