Journal of Algebra最新文献

英文中文

A generalisation of the pencil of Kuribayashi-Komiya quartics Kuribayashi-Komiya四分位数铅笔的推广

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-02-02 DOI: 10.1016/j.jalgebra.2026.01.033

Valentina Moreno Vega, Sebastián Reyes-Carocca

The pencil of Kuribayashi-Komiya quartics

x^{4} + y^{4} + z^{4} + t (x^{2} y^{2} + x^{2} z^{2} + y^{2} z^{2}) = 0 where t \in \bar{C}

is a complex one-dimensional family of Riemann surfaces of genus three endowed with a group of automorphisms isomorphic to the symmetric group of order twenty-four. This pencil has been extensively studied from different points of view.

This paper is aimed at studying, for each prime number

p ⩾ 5

, the pencil of generalised Kuribayashi-Komiya curves

F_{p}

, given by the curves

x^{2 p} + y^{2 p} + z^{2 p} + t (x^{p} y^{p} + x^{p} z^{p} + y^{p} z^{p}) = 0 where t \in \bar{C} .

We determine the full automorphism group G of each smooth member

X \in F_{p}

and study the action of G and of its subgroups on X. In particular, we show that no member of the pencil is hyperelliptic. As a by-product, we derive a classification of all those Riemann surfaces of genus

(p - 1) (2 p - 1)

that are endowed with a group of automorphisms isomorphic to the full automorphism group of the generic smooth member of

F_{p}

Kuribayashi-Komiya四边形x4+y4+z4+t(x2y2+x2z2+y2z2)=0的铅笔，其中t∈C¯是一个复一维的三属黎曼曲面族，具有与24阶对称群同构的自同构群。人们从不同的角度对这种铅笔进行了广泛的研究。本文旨在研究，对于每个素数p小于5，广义Kuribayashi-Komiya曲线Fp的铅笔，由曲线x2p+y2p+z2p+t(xpyp+xpzp+ypzp)=0给出，其中t∈C¯。我们确定了每个光滑元素X∈Fp的全自同构群G，并研究了G及其子群对X的作用。特别地，我们证明了铅笔上没有一个元素是超椭圆的。作为副产物，我们导出了所有具有与Fp的一般光滑元素的全自同构群同构的（p−1）（2p−1）属的黎曼曲面的分类。

引用次数: 0

A polynomial basis for the stuffle algebra and its applications 填充代数的多项式基及其应用

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jalgebra.2026.01.026

Tuan Ngo Dac , Gia Vuong Nguyen Chu , Lan Huong Pham

In this paper we construct a polynomial basis for the stuffle algebra over a field of characteristic

p > 0

. As an application we derive the transcendence degree for multiple zeta values in positive characteristic of small weights. To our knowledge, the only known result is the case of weight 2 which was proved by Mishiba using a completely different approach.

本文构造了特征为p>；0的域上的填充代数的多项式基。作为一个应用，我们导出了小权重正特征中多个zeta值的超越度。据我们所知，唯一已知的结果是权值2的情况，它是由三叶用一种完全不同的方法证明的。

引用次数: 0

Lannes' T-functor and mod-p cohomology of profinite groups 无限群的lanes t函子与模p上同调

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jalgebra.2026.01.024

Marco Boggi

The Lannes-Quillen theorem relates the mod-p cohomology of a finite group G with the mod-p cohomology of centralizers of abelian elementary p-subgroups of G, for

p > 0

a prime number. This theorem was extended to profinite groups whose mod-p cohomology algebra is finitely generated by Henn. In a weaker form, the Lannes-Quillen theorem was then extended by Symonds to arbitrary profinite groups. Building on Symonds' result, we formulate and prove a full version of this theorem for all profinite groups. For this purpose, we develop a theory of products for families of discrete torsion modules, parameterized by a profinite space¹, which is dual, in a very precise sense, to the theory of coproducts for families of profinite modules, parameterized by a profinite space, developed by Haran, Melnikov and Ribes. In the last section, we give applications to the problem of conjugacy separability of p-torsion elements and finite p-subgroups.

lanes - quillen定理将有限群G的模p上同调与G的阿贝尔初等p子群的中心中心的模p上同调联系起来，对于素数p>；0。将该定理推广到模p上同调代数由Henn有限生成的无限群。在一个较弱的形式下，雷恩-奎伦定理被西蒙兹推广到任意无限群。在Symonds结果的基础上，我们对所有无限群表述并证明了这个定理的完整版本。为此，我们发展了一个由无限空间参数化的离散扭转模族的积理论，在非常精确的意义上，它与由Haran， Melnikov和Ribes发展的由无限空间参数化的无限模族的余积理论是对偶的。在最后一节中，我们给出了p-扭转元和有限p-子群的共轭可分性问题的应用。

引用次数: 0

Three homological invariants under cleft extensions 裂扩张下的三个同调不变量

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jalgebra.2026.01.032

Yajun Ma , Junling Zheng , Yu-Zhe Liu

In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.

本文研究了阿贝尔范畴的裂隙扩展下的Igusa-Todorov距离、扩展和Rouquier维数的行为。我们将结果应用于森田上下文环、平凡扩展环、张量环和箭头去除。

引用次数: 0

Character tables are ideal Perron similarities 字符表是理想的Perron相似性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-02-19 DOI: 10.1016/j.jalgebra.2026.02.004

David Z. Gershnik, Alexander J. Lewis, Pietro Paparella

An invertible matrix is called a Perron similarity if it diagonalizes an irreducible, nonnegative matrix. Each Perron similarity gives a nontrivial polyhedral cone, called the spectracone, and polytope, called the spectratope, of realizable spectra (thought of as vectors in complex Euclidean space). A Perron similarity is called ideal if its spectratope coincides with the conical hulls of its rows. Identifying ideal Perron similarities is of great interest in the pursuit of the longstanding nonnegative inverse eigenvalue problem.

In this work, it is shown that the character table of a finite group is an ideal Perron similarity. In addition to expanding ideal Perron similarities to include a broad class of matrices, the results unify previous works into a single, theoretical framework.

It is demonstrated that the spectracone can be described by finitely-many group-theoretic inequalities. When the character table is real, we derive a group-theoretic formula for the volume of the projected Perron spectratope, which is a simplex. Finally, an implication for further research is given.

一个可逆矩阵如果对角化了一个不可约的非负矩阵，就称为Perron相似。每个Perron相似性给出了一个非平凡的多面体圆锥，称为谱体，以及可实现光谱的多面体，称为谱体（被认为是复欧几里得空间中的向量）。如果Perron相似度的光谱与排列的圆锥形外壳一致，则称为理想相似度。识别理想的Perron相似性是长期存在的非负特征值反问题的重要研究方向。本文证明了有限群的特征表是一个理想的Perron相似。除了将理想的Perron相似性扩展到包括广泛的矩阵类别之外，这些结果将以前的工作统一到一个单一的理论框架中。证明了谱元可以用有限多个群论不等式来描述。在特征表为实的情况下，导出了投影佩龙光谱体积的单形群论公式。最后，对进一步的研究进行了展望。

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引用次数: 0

Baker-Beynon duality beyond semisimplicity 贝克-贝农二象性超越了半简单性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-02-09 DOI: 10.1016/j.jalgebra.2026.02.002

Luca Carai , Serafina Lapenta , Luca Spada

Combining tools from category theory, model theory, and non-standard analysis we extend Baker-Beynon dualities to the classes of all Abelian ℓ-groups and all Riesz spaces (also known as vector lattices). The extended dualities have a strong geometrical flavor, as they involve a non-standard version of the category of polyhedral cones and piecewise (homogeneous) linear maps between them. We further show that our dualities are induced by the functor Spec, once it is understood how to endow it with “coordinates” in some ultrapower

U

R

. This also allows us to characterize the topological spaces arising as spectra of Abelian ℓ-groups and Riesz spaces as certain subspaces of

U^{κ}

endowed with the Zariski topology given by definable functions in their respective languages. Furthermore, we provide some applications of the extended duality by characterizing, in geometrical terms, semisimplicity, Archimedeanity, and the existence of weak and strong order-units. Finally, we show that our dualities afford a neat and simpler proof of Panti's celebrated characterization of the prime ideals in free Abelian ℓ-groups and Riesz spaces.

结合范畴论、模型论和非标准分析的工具，我们将Baker-Beynon对偶扩展到所有阿贝尔群和所有Riesz空间（也称为向量格）的类。扩展对偶具有强烈的几何风味，因为它们涉及多面体锥类别的非标准版本以及它们之间的分段（齐次）线性映射。我们进一步证明了我们的对偶性是由函子Spec引起的，一旦我们理解了如何赋予它在某些超幂U (r)中的“坐标”，这也允许我们将作为Abelian -群的谱产生的拓扑空间和Riesz空间表征为具有各自语言的可定义函数给出的Zariski拓扑的Uκ的某些子空间。在此基础上，给出了扩展对偶的一些应用，从几何角度刻画了半简单性、阿基米德性以及弱、强序单元的存在性。最后，我们证明了我们的对偶提供了Panti关于自由阿贝尔群和Riesz空间中素数理想的著名刻画的简洁和简单的证明。

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引用次数: 0

The ring of differential operators on a quantized flag manifold 量子化标志流形上的微分算子环

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jalgebra.2026.01.023

Toshiyuki Tanisaki

We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra (q-analogue of boson).

建立了量子化标志流形上的微分算子环的一些性质。特别地，我们用量子Weyl代数（玻色子的q-analogue）给出了它在仿射开子集上的局域性的显式描述。

引用次数: 0

The splitting of generalisations of the Fadell-Neuwirth short exact sequence Fadell-Neuwirth短精确序列推广的分裂

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-02-02 DOI: 10.1016/j.jalgebra.2026.01.039

Daciberg Lima Gonçalves , John Guaschi , Carolina de Miranda e Pereiro

We study some generalisations to mixed braid groups of the Fadell-Neuwirth short exact sequence and the possible splitting of this sequence. In certain cases, we determine conditions under which the projection from the mixed braid group

B_{n_{1}, \dots, n_{k}} (M)

B_{n_{1}, \dots, n_{k - q}} (M)

admits a section, where M is either the torus or the Klein bottle,

n_{1}, \dots, n_{k}, q \in N

, and

1 \leq q \leq k - 1

. For

k \geq 2

and

q = k - 1

, we show that this projection admits a section if and only if

n_{1}

divides

n_{i}

for all

i = 2, \dots, k

. We present some partial conclusions in the case

k \geq 3

and

q = 1

. To obtain our results, we compute and make use of suitable mixed braid groups of M, as well as certain key quotients that play a central rôle in our analysis.

研究了Fadell-Neuwirth短精确序列混合辫群的一些推广及其可能的分裂。在某些情况下，我们确定了从混合编织群Bn1，…，nk(M)到Bn1，…，nk−q(M)的投影允许一个截面的条件，其中M为环面或克莱因瓶，n1，…，nk,q∈N，且1≤q≤k−1。对于k≥2且q=k−1，我们证明当且仅当n1除ni时，对于所有i=2，…，k，这个投影允许一个截面。在k≥3且q=1的情况下，给出了部分结论。为了得到我们的结果，我们计算并利用了合适的M的混合编织组，以及在我们的分析中起中心作用的某些关键商rôle。

引用次数: 0

On complete integral closedness of the p-adic completion of absolute integral closure 绝对积分闭包的p进补全的完全积分闭包性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-02-02 DOI: 10.1016/j.jalgebra.2026.01.037

Raymond Heitmann , Linquan Ma

Fix a prime p and let

(R, m)

be a Noetherian complete local domain of mixed characteristic

(0, p)

with fraction field K. Let

R^{+}

denote the absolute integral closure of R, which is the integral closure of R in an algebraic closure

\overline{K}

of K. The first author has shown that

\hat{R^{+}}

, the p-adic completion of

R^{+}

, is an integral domain. In this paper, we prove that

\hat{R^{+}}

is completely integrally closed in

\hat{R^{+}} \otimes_{R^{+}} \overline{K}

, but

\hat{R^{+}}

is not completely integrally closed in its own fraction field when

\dim (R) \geq 2

定一个素数p，设（R,m）是一个具有分数域K的混合特征（0,p）的noether完备局部域，设R+表示R的绝对积分闭包，它是R在K的代数闭包K中的积分闭包。第一作者证明了R+的p进补全R+ -是一个积分域。本文证明了R+ R+K中R+是完全积分闭的，但是当dim (R)≥2时，R+在它自己的分数域中不是完全积分闭的。

引用次数: 0

Deformations and homotopy theory of Nijenhuis associative algebras Nijenhuis结合代数的变形与同伦理论

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jalgebra.2025.12.032

Chao Song , Kai Wang , Yuanyuan Zhang , Guodong Zhou

This paper is the first in a series of works devoted to an operadic study of Nijenhuis structures, focusing on Nijenhuis associative algebras. We introduce the concept of homotopy Nijenhuis associative algebras and demonstrate that the differential graded (=dg) operad

{NjA}_{\infty}

governing these structures serves as the minimal model of the operad

NjA

for Nijenhuis associative algebras. Additionally, we determine the Koszul dual homotopy cooperad of

NjA

. We construct an

L_{\infty}

-algebra that controls the simultaneous deformations of associative products and Nijenhuis operators. The Maurer-Cartan elements of this

L_{\infty}

-algebra correspond bijectively to Nijenhuis associative algebra structures. From this, we derive a cochain complex (deformation complex) and an associated cohomology theory of Nijenhuis associative algebras. Finally, we explore the connection between homotopy relative Rota-Baxter associative algebras of weight 0 and homotopy Nijenhuis associative algebras. A sequel to this work will extend the study to Nijenhuis Lie algebras, with applications to Nijenhuis geometry.

这篇论文是一系列致力于尼延惠斯结构的操作性研究的作品中的第一篇，重点是尼延惠斯结合代数。我们引入了同伦Nijenhuis结合代数的概念，并证明了控制这些结构的微分梯度（=dg）算子NjA∞作为Nijenhuis结合代数的算子NjA的最小模型。此外，我们还确定了NjA的Koszul对偶同伦。我们构造了一个L∞-代数来控制关联积和Nijenhuis算子的同时变形。该L∞代数的Maurer-Cartan元客观上对应于Nijenhuis联想代数结构。由此，我们得到了Nijenhuis结合代数的一个协链复形（变形复形）和一个相关上同调理论。最后，我们探讨了权值为0的同伦相对Rota-Baxter结合代数与同伦Nijenhuis结合代数之间的联系。这项工作的续集将把研究扩展到尼延惠斯李代数，并应用于尼延惠斯几何。

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引用次数: 0

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Journal of Algebra

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