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Instantons with continuous conformal symmetries 具有连续共形对称性的瞬子
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-10-06 DOI: 10.1016/j.geomphys.2025.105670
C.J. Lang
Throughout this paper, we comprehensively study instantons with every kind of continuous conformal symmetry. Examples of these objects are hard to come by due to non-linear constraints. However, by applying previous work on moduli spaces, we introduce a linear constraint, whose solution greatly simplifies these non-linear constraints. This simplification not only allows us to easily find a plethora of novel instantons with various continuous conformal symmetries and higher rank structure groups, it also provides a framework for classifying such symmetric objects. We also prove that the basic instanton is essentially the only instanton with two particular kinds of conformal symmetry. Additionally, we discuss the connections between instantons with continuous symmetries and other gauge-theoretic objects: hyperbolic and singular monopoles as well as hyperbolic analogues to Higgs bundles and Nahm data.
本文全面研究了具有各种连续共形对称的实例。由于非线性约束，这些对象的例子很难得到。然而，通过应用先前在模空间上的工作，我们引入了一个线性约束，它的解极大地简化了这些非线性约束。这种简化不仅使我们能够很容易地找到大量具有各种连续共形对称和高阶结构群的新实例，而且还为分类这些对称对象提供了一个框架。我们还证明了基本瞬子本质上是唯一具有两种特定共形对称性的瞬子。此外，我们还讨论了具有连续对称性的瞬子与其他规范理论对象之间的联系：双曲单极子和奇异单极子，以及与希格斯束和纳姆数据类似的双曲单极子。
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引用次数: 0
Moduli space of orthogonal bundles of even rank and theta functions 偶秩函数和正交束的模空间
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-10-02 DOI: 10.1016/j.geomphys.2025.105668
Hacen Zelaci
In this note, we show that the space of theta functions of the Pfaffian line bundle over the moduli space of stable SO2m-bundles has dimension one. Using the Hitchin system, we construct a dominant rational map from a principally polarized Prym variety to each connected component of this moduli space.
本文证明了Pfaffian线束在稳定so2m -束的模空间上的函数空间的维数为1。利用Hitchin系统，构造了一个主极化Prym变换到该模空间的每个连通分量的占优有理映射。
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引用次数: 0
Cohomotopy and flux quantization in M-theory m理论中的上同伦与通量量子化
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-30 DOI: 10.1016/j.geomphys.2025.105667
Daniel Grady
We identify some of the k-invariants for the Postnikov tower of the stable and unstable 4-sphere. Assuming the stable Hypothesis H of Fiorenza–Sati–Schreiber, we use the resulting obstruction theory to prove that the Chern–Simons term in the effective action of M-theory is well defined. In particular, we do not assume the presence of an E8-gauge field.
我们确定了稳定和不稳定4球的波斯特尼科夫塔的若干k不变量。假设fiorenza - satii - schreiber的稳定假设H，我们利用由此得到的阻碍理论证明了m理论有效作用中的chen - simons项是定义良好的。特别是，我们不假设存在e8规格的字段。
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引用次数: 0
Log-concavity of the Grothendieck classes of banana graphs and clasped necklaces 香蕉图和项链的Grothendieck类的对数凹性
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-29 DOI: 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 M0,4 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.
单调图的Grothendieck类满足递归关系，可以表示为模空间M0,4类中系数为非负整数的多项式，推测为对数凹。在本文中，我们研究了香蕉图的Grothendieck类的对数凹性和超对数凹性，以及递归关系中所涉及的三族多项式。我们证明了这四种图都是对数凹的，建立了香蕉图的对数凹猜想的特殊情况。此外，我们还引入了无限族的夹紧项链，即用一串m-香蕉代替一条2-香蕉的边得到的密子图。利用递归关系，我们显式地计算了锁扣项链的类，并证明了它们也是对数凹的。
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引用次数: 0
Super Kupershmidt operator and the Yang-Baxter equation in Malcev superalgebras Malcev超代数中的超级Kupershmidt算子和Yang-Baxter方程
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-29 DOI: 10.1016/j.geomphys.2025.105663
Yinuo Zhao , Liangyun Chen
In this paper, we show the relationship between skew-symmetric solutions of the Yang-Baxter equation (YBE) and super Kupershmidt operators of Malcev superalgebras. First, we show that a skew-supersymmetric solution of the Yang-Baxter equation on a Malcev superalgebra can be interpreted as an super Kupershmidt operator associated to the coadjoint representation. On this basis, when considering non-degenerate skew-symmetric solutions of the Yang-Baxter equation, this connection can be enhanced with symplectic forms. We also show that super Kupershmidt operators associated with a general representation could give skew-symmetric solutions of the Yang-Baxter equation on certain semi-direct products of Malcev superalgebras. What's more, we reveal that in the case of pre-Malcev superalgebras, We can get similar results between the Yang-Baxter equation and super Kupershmidt operators.
本文给出了Yang-Baxter方程（YBE）的偏对称解与Malcev超代数的超Kupershmidt算子之间的关系。首先，我们证明了Malcev超代数上Yang-Baxter方程的偏超对称解可以被解释为与协表示相关的超Kupershmidt算子。在此基础上，当考虑Yang-Baxter方程的非简并偏对称解时，这种联系可以用辛形式增强。我们还证明了与一般表示相关联的超Kupershmidt算子可以给出Malcev超代数的半直积上的Yang-Baxter方程的偏对称解。此外，我们揭示了在pre-Malcev超代数的情况下，我们可以在Yang-Baxter方程和超级Kupershmidt算子之间得到类似的结果。
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引用次数: 0
Connections and Higgs bundles on curves defined over a number field 数域上曲线上的连接和希格斯束
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-29 DOI: 10.1016/j.geomphys.2025.105664
Indranil Biswas , Sudarshan Gurjar
Let X0 be an irreducible smooth projective curve defined over Q‾ and E a vector bundle on X0. We give a criterion for connections on the base change E⊗Q‾C⟶X0×SpecQ‾SpecC to C to be the base change of some connection on E. A similar criterion is given for Higgs fields on E⊗Q‾C
设X0是一条定义在Q面上的不可约光滑投影曲线，E是X0上的向量束。我们给出了一个关于E⊗Q - C - X0×SpecQ的连接的基变化的准则E⊗Q - C上的连接是E上的一些连接的基变化的准则。对于E⊗Q - C上的希格斯场也给出了类似的准则
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引用次数: 0
Maurer–Cartan elements on holomorphic Poisson manifolds 全纯泊松流形上的Maurer-Cartan元
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-26 DOI: 10.1016/j.geomphys.2025.105665
Youming Chen, Liping Su
In this paper, we consider the Maurer–Cartan equation on holomorphic Poisson manifolds. For a differential graded Lie algebra (DGLA) associated with a holomorphic Poisson structure, we show the existence of its Maurer–Cartan elements under the assumption of the ∂∂¯-lemma or ∂π∂¯-lemma, and discuss their uniqueness under gauge equivalence with certain topological restrictions.
本文研究了全纯泊松流形上的Maurer-Cartan方程。对于与全纯泊松结构相关的微分梯度李代数（DGLA），在∂∂¯-外理或∂π∂¯-外理的假设下，证明了其Maurer-Cartan元的存在性，并讨论了它们在具有一定拓扑限制的规范等价下的唯一性。
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引用次数: 0
Post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations for the Heisenberg-Virasoro algebra Heisenberg-Virasoro代数的后李代数结构，Rota-Baxter算子和Yang-Baxter方程
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-24 DOI: 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.
在本文中，我们给出了在Heisenberg-Virasoro代数上的梯度后李代数结构的完整表征。作为应用，我们研究了Heisenberg-Virasoro代数上的齐次Rota-Baxter算子（权值为1）和形式经典Yang-Baxter方程的一类解。
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引用次数: 0
Hyperbolic Monge–Ampère systems with S1 = 0 具有S1 = 的双曲monge - ampantere系统
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105655
Yuhao Hu
For hyperbolic Monge–Ampère systems, a well-known solution of the equivalence problem yields two invariant tensors, S1 and S2, defined on the underlying 5-manifold, where S2=0 characterizes systems that are Euler–Lagrange. In this article, we consider the ‘opposite’ case, S1=0, and show that the local generality of such systems is ‘2 arbitrary functions of 3 variables’. In addition, we classify all S1=0 systems with cohomogeneity at most one, which turn out to be linear up to contact transformations.
对于双曲monge - ampantere系统，一个众所周知的等价问题的解产生了两个不变张量，S1和S2，定义在基础的5流形上，其中S2=0表征欧拉-拉格朗日系统。在本文中，我们考虑“相反”的情况，S1=0，并证明了这种系统的局部一般性是“2个3变量的任意函数”。此外，我们对所有最多有一个同质性的S1=0系统进行了分类，这些系统在接触变换之前都是线性的。
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引用次数: 0
On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and Tempesta–Tondo conjecture 小维算子域的Jordan-Chevalley分解问题及Tempesta-Tondo猜想
IF 1.2 3区 数学 Q1 MATHEMATICS
Journal of Geometry and Physics
Pub Date : 2025-09-24 DOI: 10.1016/j.geomphys.2025.105656
Alexey V. Bolsinov , Andrey Yu. Konyaev , Vladimir S. Matveev
We explore the Jordan–Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field L, similar to a nilpotent Jordan block, to possess local coordinates in which L takes a strictly upper triangular form. We prove the Tempesta–Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type.
研究了小维算子域的Jordan-Chevalley分解问题。在三维和四维中，我们找到了类似于幂零约当块的算子域L具有局部坐标的张量条件，其中L为严格上三角形式。证明了Frölicher-Nijenhuis型高阶括号的Tempesta-Tondo猜想。
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