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Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras 非平凡可解三维李代数的广义可积顶
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-19 DOI: 10.1016/j.geomphys.2025.105572
Jinrong Bao
{"title":"Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras","authors":"Jinrong Bao","doi":"10.1016/j.geomphys.2025.105572","DOIUrl":"10.1016/j.geomphys.2025.105572","url":null,"abstract":"<div><div>The goal of this paper is to study and construct analogues of integrable tops related to three dimensional solvable Lie algebras in Bianchi types. We consider the semi-direct products of three dimensional solvable Lie algebras <span><math><mi>g</mi></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with respect to the natural representation. This representation and its dual are not isomorphic, so we discuss them separately. We find some integrable cases with explicit description.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105572"},"PeriodicalIF":1.6,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489563","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
A proper 1-cocycle on a Podleś sphere 波德莱球上的一个合适的1-环
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-19 DOI: 10.1016/j.geomphys.2025.105571
Masato Tanaka
{"title":"A proper 1-cocycle on a Podleś sphere","authors":"Masato Tanaka","doi":"10.1016/j.geomphys.2025.105571","DOIUrl":"10.1016/j.geomphys.2025.105571","url":null,"abstract":"<div><div>We define 1-cocycles on coideal ⁎-subalgebras of CQG Hopf ⁎-algebras and consider the condition for them to extend to 1-cocycles on Drinfeld double coideals. We construct a 1-cocycle on a Podleś sphere which extends to a 1-cocycle of the Drinfeld double coideal, which is considered as a quantization of <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></math></span>. We prove that this 1-cocycle is proper.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105571"},"PeriodicalIF":1.6,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489773","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
A note on Ricci soliton components of locally product manifolds 局部积流形的Ricci孤子分量的注记
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-11 DOI: 10.1016/j.geomphys.2025.105569
Arif Salimov
{"title":"A note on Ricci soliton components of locally product manifolds","authors":"Arif Salimov","doi":"10.1016/j.geomphys.2025.105569","DOIUrl":"10.1016/j.geomphys.2025.105569","url":null,"abstract":"<div><div>Ricci solitons components of locally product manifold are considered and a new explicit formula for Ricci tensor in the locally decomposable Riemannian manifold was found in the case where the soliton vector fields are components of a decomposable vector field.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105569"},"PeriodicalIF":1.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263849","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
Formal languages, spin systems, and quasicrystals 形式语言、自旋系统和准晶体
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-11 DOI: 10.1016/j.geomphys.2025.105568
Francesca Fernandes , Matilde Marcolli
{"title":"Formal languages, spin systems, and quasicrystals","authors":"Francesca Fernandes ,&nbsp;Matilde Marcolli","doi":"10.1016/j.geomphys.2025.105568","DOIUrl":"10.1016/j.geomphys.2025.105568","url":null,"abstract":"<div><div>We present a categorical formalism for context-free languages with morphisms given by correspondences obtained from rational transductions. We show that D0L-systems are a special case of the correspondences that define morphisms in this category. We construct a functorial mapping to aperiodic spin chains. We then generalize this construction to a class of mildly context sensitive grammars, the multiple-context-free grammars (MCFG), with a similar functorial mapping to spin systems in higher dimensions, with Boltzmann weights describing interacting spins on vertices of hypercubes. We show that a particular motivating example for this general construction is provided by the Korepin completely integrable model on the icosahedral quasicrystal, which we construct as the spin system associated to a multiple-context-free grammar describing the geometry of the Ammann planes quasilattice. We review the main properties of this spin system, including solvability, bulk free energy, and criticality, based on results of Baxter and the known relation to the Zamolodchikov tetrahedron equation, and we show that the latter has a generalization for the Boltzmann weights on hypercubes of the spin systems associated to more general MCFGs in terms of two dual cubulations of the <em>n</em>-simplex. We formulate analogous questions about bulk free energy and criticality for our construction of spin systems.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105568"},"PeriodicalIF":1.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322410","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 reduction of symplectic Lefschetz-Bott fibration 关于辛Lefschetz-Bott纤颤的还原
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-10 DOI: 10.1016/j.geomphys.2025.105485
Hao Ding
{"title":"On the reduction of symplectic Lefschetz-Bott fibration","authors":"Hao Ding","doi":"10.1016/j.geomphys.2025.105485","DOIUrl":"10.1016/j.geomphys.2025.105485","url":null,"abstract":"<div><div>We give a ‘symplectic Lefschetz-Bott fibration commutes with reduction’ theorem for equivariant fibered Dehn twists along spherically fibered coisotropic submanifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105485"},"PeriodicalIF":1.6,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263848","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
The Integration Problem for principal connections 主体连接的集成问题
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-10 DOI: 10.1016/j.geomphys.2025.105566
Javier Fernández , Francisco Kordon
{"title":"The Integration Problem for principal connections","authors":"Javier Fernández ,&nbsp;Francisco Kordon","doi":"10.1016/j.geomphys.2025.105566","DOIUrl":"10.1016/j.geomphys.2025.105566","url":null,"abstract":"<div><div>In this paper we introduce the Integration Problem for principal connections. Just as a principal connection on a principal <em>G</em>-bundle <span><math><mi>ϕ</mi><mo>:</mo><mi>Q</mi><mo>→</mo><mi>M</mi></math></span> may be used to split <em>TQ</em> into horizontal and vertical subbundles, a discrete connection may be used to split <span><math><mi>Q</mi><mo>×</mo><mi>Q</mi></math></span> into horizontal and vertical submanifolds. All discrete connections induce a connection on the same principal bundle via a process known as the Lie or derivative functor. The Integration Problem consists of describing, for a principal connection <span><math><mi>A</mi></math></span>, the set of all discrete connections whose associated connection is <span><math><mi>A</mi></math></span>. Our first result is that for <em>flat</em> principal connections, the Integration Problem has a unique solution among the <em>flat</em> discrete connections. More broadly, we prove that the existence part of the Integration Problem always has a solution that needs not be unique. We also see that, when <em>G</em> is abelian, given compatible continuous and discrete curvatures the Integration Problem has a unique solution constrained by those curvatures. Last, extending the notion of discrete connection, we introduce a notion of discrete secondary Ehresmann connection associated to suitable morphisms of local Lie groupoids; then we state the Integration Problem in this context, proving that in the flat case, there is an essentially unique solution.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105566"},"PeriodicalIF":1.6,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290997","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 Đurđević approach to quantum principal bundles 关于Đurđević量子主束的方法
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-10 DOI: 10.1016/j.geomphys.2025.105567
Antonio Del Donno , Emanuele Latini , Thomas Weber
{"title":"On the Đurđević approach to quantum principal bundles","authors":"Antonio Del Donno ,&nbsp;Emanuele Latini ,&nbsp;Thomas Weber","doi":"10.1016/j.geomphys.2025.105567","DOIUrl":"10.1016/j.geomphys.2025.105567","url":null,"abstract":"<div><div>We revisit and extend the Đurđević theory of complete calculi on quantum principal bundles. In this setting one naturally obtains a graded Hopf–Galois extension of the higher order calculus and an intrinsic decomposition of degree 1-forms into horizontal and vertical forms. This proposal is appealing, since it is consistently equipped with a canonical braiding and exactness of the Atiyah sequence is guaranteed. Moreover, we provide examples of complete calculi, including the noncommutative 2-torus, the quantum Hopf fibration and differential calculi on crossed product algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105567"},"PeriodicalIF":1.6,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144272033","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
Modular vector fields in non-commutative geometry 非交换几何中的模向量场
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-09 DOI: 10.1016/j.geomphys.2025.105565
Toyo Taniguchi
{"title":"Modular vector fields in non-commutative geometry","authors":"Toyo Taniguchi","doi":"10.1016/j.geomphys.2025.105565","DOIUrl":"10.1016/j.geomphys.2025.105565","url":null,"abstract":"<div><div>We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation <em>μ</em> similar to the one obtained by Alekseev–Kawazumi–Kuno–Naef and the author.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105565"},"PeriodicalIF":1.6,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254816","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
Manin pairs and moment maps revisited 重新审视了许多对和矩图
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-04 DOI: 10.1016/j.geomphys.2025.105556
Eckhard Meinrenken, Selim Tawfik
{"title":"Manin pairs and moment maps revisited","authors":"Eckhard Meinrenken,&nbsp;Selim Tawfik","doi":"10.1016/j.geomphys.2025.105556","DOIUrl":"10.1016/j.geomphys.2025.105556","url":null,"abstract":"<div><div>The notion of quasi-Poisson <em>G</em>-spaces with <span><math><mi>D</mi><mo>/</mo><mi>G</mi></math></span>-valued moment maps was introduced by Alekseev and Kosmann-Schwarzbach in 1999. Our main result is a <em>Lifting Theorem</em>, establishing a bijective correspondence between the categories of quasi-Poisson <em>G</em>-spaces with <span><math><mi>D</mi><mo>/</mo><mi>G</mi></math></span>-valued moment maps and of quasi-Poisson <span><math><mi>G</mi><mo>×</mo><mi>G</mi></math></span>-spaces with <em>D</em>-valued moment maps. Using this result, we give simple constructions of fusion and conjugation for these spaces, and new examples coming from moduli spaces.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105556"},"PeriodicalIF":1.6,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263847","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
Threefold nature of graded vector bundles 梯度矢量束的三重性质
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-06-04 DOI: 10.1016/j.geomphys.2025.105557
Rudolf Šmolka, Jan Vysoký
{"title":"Threefold nature of graded vector bundles","authors":"Rudolf Šmolka,&nbsp;Jan Vysoký","doi":"10.1016/j.geomphys.2025.105557","DOIUrl":"10.1016/j.geomphys.2025.105557","url":null,"abstract":"<div><div>Graded vector bundles over a given <span><math><mi>Z</mi></math></span>-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules over the algebra of global functions on the base graded manifold, or locally trivial graded manifolds with a suitable linear structure. We argue that all three approaches are the same. More precisely, the respective categories are proved to be equivalent.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105557"},"PeriodicalIF":1.6,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241254","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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