Journal of Geometry and Physics最新文献

英文中文

Quantization of web geometry: Semisymmetrization of linear quantum quasigroups 网几何的量化：线性量子拟群的半对称化

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-02-02 DOI: 10.1016/j.geomphys.2026.105781

Jonathan D.H. Smith

Classical quasigroups coordinatize structures called 3-nets in combinatorics, and 3-webs in geometry. The coordinatization is up to isotopy, a relation coarser than isomorphism. The semisymmetrization of a classical quasigroup is built on the cube of the underlying set of the quasigroup. Isotopic quasigroups have isomorphic semisymmetrizations.

Quantum quasigroups provide a self-dual unification (with both a multiplication and a comultiplication) of quasigroups and Hopf algebras, in the general setting of symmetric monoidal categories. Linear quantum quasigroups are quantum quasigroups in categories of vector spaces or modules over a commutative ring, with the direct sum as the Cartesian monoidal product.

With a view to addressing the quantization of web geometry, the paper determines linear quantum quasigroup structures that provide comultiplications to extend the semisymmetrization multiplication of a linear quasigroup. In particular, if the linear quasigroup structure comes from a real or complex affine plane, a complete classification of the quantum semisymmetric comultiplications is provided, based on the solution of a system of cubic equations.

经典拟群协调的结构在组合学中称为3-网，在几何中称为3-网。这种配位达到了同位素关系，这是一种比同构关系更粗糙的关系。一个经典拟群的半对称是建立在拟群的下集的立方上的。同位素准群具有同构半对称性。在对称一元范畴的一般情况下，量子拟群提供了拟群和Hopf代数的自对偶统一（既有乘法也有乘法）。线性量子拟群是交换环上向量空间或模范畴内的量子拟群，其和为笛卡尔单轴积。为了解决网几何的量子化问题，本文确定了线性量子拟群结构，该结构提供了扩展线性拟群的半对称乘法的乘法。特别地，如果线性拟群结构来自实或复仿射平面，则基于三次方程组的解，给出了量子半对称乘法的完整分类。

{"title":"Quantization of web geometry: Semisymmetrization of linear quantum quasigroups","authors":"Jonathan D.H. Smith","doi":"10.1016/j.geomphys.2026.105781","DOIUrl":"10.1016/j.geomphys.2026.105781","url":null,"abstract":"<div><div>Classical quasigroups coordinatize structures called 3-nets in combinatorics, and 3-webs in geometry. The coordinatization is up to isotopy, a relation coarser than isomorphism. The semisymmetrization of a classical quasigroup is built on the cube of the underlying set of the quasigroup. Isotopic quasigroups have isomorphic semisymmetrizations.</div><div>Quantum quasigroups provide a self-dual unification (with both a multiplication and a comultiplication) of quasigroups and Hopf algebras, in the general setting of symmetric monoidal categories. Linear quantum quasigroups are quantum quasigroups in categories of vector spaces or modules over a commutative ring, with the direct sum as the Cartesian monoidal product.</div><div>With a view to addressing the quantization of web geometry, the paper determines linear quantum quasigroup structures that provide comultiplications to extend the semisymmetrization multiplication of a linear quasigroup. In particular, if the linear quasigroup structure comes from a real or complex affine plane, a complete classification of the quantum semisymmetric comultiplications is provided, based on the solution of a system of cubic equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"223 ","pages":"Article 105781"},"PeriodicalIF":1.2,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102835","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 Atiyah class of DG manifolds of amplitude +1 振幅+1的DG流形的Atiyah类

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-28 DOI: 10.1016/j.geomphys.2026.105774

Seokbong Seol

A DG manifold of amplitude +1 encodes the derived intersection of a section s and the zero section of a vector bundle E. In this paper, we compute the Atiyah class of DG manifolds of amplitude +1. In particular, we show that the Atiyah class vanishes if and only if the intersection of s with the zero section is a clean intersection. As an application, we study the Atiyah class of DG manifolds that encodes the derived intersection of two smooth manifolds.

一个振幅为+1的DG流形编码了矢量束e的截面s与零截面的导数交。本文计算了振幅为+1的DG流形的Atiyah类。特别地，我们证明Atiyah类消失当且仅当s与零截面的交点是一个干净的交点。作为应用，我们研究了编码两个光滑流形的派生交的DG流形的Atiyah类。

引用次数: 0

Moduli spaces of pentagonal subdivision tilings 五边形细分瓷砖的模空间

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-27 DOI: 10.1016/j.geomphys.2026.105773

Jinjin Liang , Erxiao Wang , Min Yan

Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two real parameter moduli space. We describe these moduli spaces in detail, to complete the classification of such tilings and to facilitate potential applications in physics and other disciplines.

五边形细分给出了球体的三个族的边到边的平铺由全等五边形。每个族形成一个两个实参数模空间。我们详细描述了这些模空间，以完成这种瓷砖的分类，并促进在物理和其他学科的潜在应用。

引用次数: 0

Remarks on structures and preservation in forced discrete mechanical systems of Routh type 劳斯型强迫离散力学系统的结构与保存

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-27 DOI: 10.1016/j.geomphys.2026.105776

Matías I. Caruso , Javier Fernández , Cora Tori , Marcela Zuccalli

We study a type of forced discrete mechanical system

(Q, L_{d}, f_{d})

—that we name of Routh type— whose (discrete) time-flow preserves a symplectic structure on

Q \times Q

. That structure arises as the pullback via the forced discrete Legendre transform of the canonical symplectic structure on

T^{⁎} Q

modified by a “magnetic term”. One example of this type of system is provided by the Lagrangian reduction of a symmetric (unforced) discrete mechanical system in the Routh style. In this particular case, we do not reduce by the full symmetry group but, rather, by an appropriate isotropy subgroup. In this context, the preserved symplectic structure can be alternatively seen as the Marsden-Weinstein reduction of the canonical symplectic structure

ω_{L_{d}}

Q \times Q

我们研究了一类强制离散机械系统(Q,Ld,fd) -我们称之为Routh型-其（离散）时间流在Q×Q上保持辛结构。该结构是通过T - Q上经“磁项”修饰的正则辛结构的强制离散勒让德变换产生的回拉。这类系统的一个例子是对称（非强制）离散机械系统的拉格朗日约简。在这种特殊情况下，我们不是通过全对称群，而是通过适当的各向同性子群进行约简。在这种情况下，保留的辛结构可以被看作是正则辛结构ωLd on Q×Q的Marsden-Weinstein约简。

{"title":"Remarks on structures and preservation in forced discrete mechanical systems of Routh type","authors":"Matías I. Caruso , Javier Fernández , Cora Tori , Marcela Zuccalli","doi":"10.1016/j.geomphys.2026.105776","DOIUrl":"10.1016/j.geomphys.2026.105776","url":null,"abstract":"<div><div>We study a type of forced discrete mechanical system <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>)</mo></math></span> —that we name of Routh type— whose (discrete) time-flow preserves a symplectic structure on <span><math><mi>Q</mi><mo>×</mo><mi>Q</mi></math></span>. That structure arises as the pullback via the forced discrete Legendre transform of the canonical symplectic structure on <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Q</mi></math></span> modified by a “magnetic term”. One example of this type of system is provided by the Lagrangian reduction of a symmetric (unforced) discrete mechanical system in the Routh style. In this particular case, we do not reduce by the full symmetry group but, rather, by an appropriate isotropy subgroup. In this context, the preserved symplectic structure can be alternatively seen as the Marsden-Weinstein reduction of the canonical symplectic structure <span><math><msub><mrow><mi>ω</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></math></span> on <span><math><mi>Q</mi><mo>×</mo><mi>Q</mi></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"223 ","pages":"Article 105776"},"PeriodicalIF":1.2,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102939","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

Loop general BMS-Kac-Moody Lie conformal algebra 环一般BMS-Kac-Moody Lie共形代数

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-27 DOI: 10.1016/j.geomphys.2026.105775

Fu Liu

In this paper, we construct two kinds of Lie conformal algebras

cgm

and

cm

, associated with the loop general BMS-Kac-Moody algebra

gm

and the loop BMS-Kac-Moody algebra

m

, respectively. The second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and

Z

-graded free intermediate series modules over these two conformal algebras are also classified.

本文构造了两类李共形代数cgm和cm，分别与环一般BMS-Kac-Moody代数gm和环BMS-Kac-Moody代数m相关联。这两个共形代数的第二上同调群是完全确定的。并对这两个共形代数上的1阶非平凡自由共形模和z阶自由中间级数模进行了分类。

引用次数: 0

Corrigendum to ‘A reconstruction theorem for Connes–Landi deformations of commutative spectral triples’ [J. Geom. Phys. 98 (2015) 82–109] 对交换谱三元组的cones - landi变形的重构定理的更正[J]。几何学。物理学报，98 (2015)82-109]

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-26 DOI: 10.1016/j.geomphys.2026.105769

Branimir Ćaćić

We strengthen the orientability condition in our definition of θ-commutative spectral triple to resolve an issue with the proof of our main theorem. In particular, we show that this corrected condition is still satisfied in the relevant commutative case.

我们在θ-可交换谱三重体的定义中加强了可定向条件，从而解决了证明主要定理的一个问题。特别地，我们证明了在相应的交换情况下，这个修正条件仍然是满足的。

引用次数: 0

Matrix integrable models associated with reduced AKNS Lax pairs 与简化AKNS Lax对相关的矩阵可积模型

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-23 DOI: 10.1016/j.geomphys.2026.105772

Wen-Xiu Ma , Chaudry Masood Khalique

Pairs of group reductions or similarity transformations involving off-diagonal block matrices are proposed and analyzed for a specific type of Ablowitz-Kaup-Newell-Segur (AKNS) matrix spectral problem. The corresponding reduced integrable hierarchies of AKNS matrix integrable models are presented, complementing the standard AKNS matrix integrable hierarchies. The Lax formulation plays a key role in generating these reduced matrix integrable models.

针对一类特殊类型的ablowitz - kap - newwell - segur （AKNS）矩阵谱问题，提出并分析了涉及非对角块矩阵的群约简或相似变换对。给出了相应的AKNS矩阵可积模型的约简可积层次，补充了标准AKNS矩阵可积层次。Lax公式在生成这些约简矩阵可积模型中起着关键作用。

引用次数: 0

Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus g 聚焦测量修正KdV格方程的超椭圆解的闭实平面曲线

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-21 DOI: 10.1016/j.geomphys.2026.105770

Shigeki Matsutani

The real part of the focusing modified Korteweg-de Vries (MKdV) equation defined over the complex field

C

is reduced to the focusing gauged MKdV (FGMKdV) equation. In this paper, we construct the real hyperelliptic solutions of FGMKdV equation in terms of data of the hyperelliptic curves of genus g and demonstrate the closed hyperelliptic plane curves of genus

g = 5

whose curvature obeys the FGMKdV equation by extending the previous results of genus three (Matsutani (2025) [29]). These are a generalization of Euler's elasticae.

将复场C上定义的调焦修正Korteweg-de Vries （MKdV）方程的实部简化为调焦测量MKdV （FGMKdV）方程。本文利用g属的超椭圆曲线的数据构造了FGMKdV方程的实超椭圆解，并通过推广先前的3属（Matsutani(2025)[29]）的结果，证明了曲率服从FGMKdV方程的g=5属的闭超椭圆平面曲线。这是欧拉弹性定理的推广。

引用次数: 0

Formal languages and TQFTs with defects 有缺陷的形式语言和tqft

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-21 DOI: 10.1016/j.geomphys.2026.105771

Luisa Boateng , Matilde Marcolli

A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms. Certain classes of subregular languages correspond to additional cohomological structures on the associated TQFTs. We also show that the construction generalizes to context-free grammars through a categorical version of the Chomsky–Schützenberger representation theorem, due to Melliès and Zeilberger. The corresponding TQFTs are then described as morphisms of colored operads on an operad of cobordisms with defects.

最近，Gustafson, Im, Kaldawy， Khovanov和linn开发了一种将带有缺陷的布尔1D TQFT分配给有限状态自动机的构造。我们证明了该构造是泛函的关于有限状态自动机的范畴与换能器作为态射。某些类的次正则语言对应于相关tqft上附加的上同调结构。我们还表明，由于melli和Zeilberger，通过乔姆斯基-施岑伯格表示定理的分类版本，该结构可以推广到上下文无关的语法。相应的tqft随后被描述为有色操作子在带有缺陷的配合子操作子上的态射。

引用次数: 0

Contact term algebras and Dijkgraaf's master equation 接触项代数与Dijkgraaf主方程

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2026-01-19 DOI: 10.1016/j.geomphys.2026.105768

Zhengping Gui , Si Li , Xinxing Tang

This paper is devoted to study integrable deformations of chiral conformal field theories on elliptic curves from the viewpoint of contact algebra. We introduce the relevant integrable condition within the framework of conformal vertex algebra, and derive the contact term relations among certain local operators. We investigate three versions of genus one partition functions and derive the contact equations. This leads to a rigorous formulation of Dijkgraaf's master equation [6] for chiral deformations.

本文从接触代数的角度研究了椭圆曲线上手性共形场理论的可积变形。在共形顶点代数的框架内引入了相关的可积条件，导出了局部算子之间的接触项关系。我们研究了三种形式的一格配分函数，并推导了接触方程。这导致手性变形的Dijkgraaf主方程[6]的严格公式。

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Geometry and Physics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀