Journal of Algebra最新文献

英文中文

Strongly closed subgroups of saturated fusion systems 饱和聚变系统的强闭子群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-12-04 DOI: 10.1016/j.jalgebra.2025.11.022

Zhencai Shen, Shengmin Zhang

Let P be a p-group and

F

a saturated fusion system over P.

F

is said to be supersolvable, if there exists a series

Γ : 1 = P_{0} ⩽ P_{1} ⩽ \dots ⩽ P_{n} = P

such that

P_{i + 1} / P_{i}

is cyclic, and

P_{i}

is strongly

F

-closed. In this paper, we firstly investigate the basic relationship between normal subgroups of finite groups and fusion systems, and secondly give criteria for

F

and

F_{P} (G)

to be supersolvable under the assumption that certain subgroups R of P are strongly closed, normal in

F

, or satisfy

F = P \cdot C_{F} (R)

. As applications of those theorems, we finally obtain several corollaries dealing with constrained fusion systems

F_{P} (G)

and finite groups.

设P是一个P群，F是一个P上的饱和聚变系统，如果存在一个级数Γ：1=P0≤P1≤⋯≤Pn=P，使得Pi+1/Pi是循环的，且Pi是强F闭的，则F是超可解的。本文首先研究了有限群的正规子群与融合系统之间的基本关系，其次给出了在P的某些子群R强闭、在F中正规或满足F=P⋅CF(R)的条件下F和FP(G)是超可解的判据。作为这些定理的应用，我们最后得到了关于约束融合系统FP(G)和有限群的几个推论。

引用次数: 0

On defectless unibranched simple extensions, complete distinguished chains and certain stability results 关于无缺陷单支简单扩展，完全区分链和一定的稳定性结果

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-12-03 DOI: 10.1016/j.jalgebra.2025.10.059

Arpan Dutta, Rumi Ghosh

Let

(K, v)

be a valued field. Take an extension of v to a fixed algebraic closure

\overline{K}

of K. In this paper we show that an element

a \in \overline{K}

admits a complete distinguished chain over K if and only if the extension

(K (a) | K, v)

is unibranched and defectless. This characterization generalizes the known result in the henselian case. In particular, our result shows that if a admits a complete distinguished chain over K, then it also admits one over the henselization

K^{h}

; however the converse may not be true. The main tool employed in our analysis is the stability of the j-invariant associated to a valuation transcendental extension under passage to the henselization.

We also explore the stability of defectless simple extensions in the following sense: let

(K (X) | K, w)

be a valuation transcendental extension with a pair of definition

(b, γ)

. Assume that either

(K (b) | K, v)

is a defectless extension, or that

f (X)

is a key polynomial for

(K (X) | K, w)

, where

f (X)

is the minimal polynomial of b over K. We show that then the extension

(K (b, X) | K (X), w)

is defectless. In particular, the extension

(K (b, X) | K (X), w)

is always defectless whenever

(b, γ)

is a minimal pair of definition for w over K.

设（K,v）是一个值域。取v对K的一个固定代数闭包K的扩展。本文证明了一个元素a∈K在K上存在一个完全的可区分链，当且仅当扩展（K(a)|K,v）是无分支且无缺陷的。这一特征概括了亨塞利安案例中的已知结果。特别地，我们的结果表明，如果a在K上有一个完全的区别链，那么它在h上也有一个区别链；然而，反过来可能不成立。在我们的分析中使用的主要工具是j不变量的稳定性，该不变量与通过到henselization的估值超越扩展相关。我们还在以下意义上探讨了无缺陷简单扩展的稳定性：设（K(X)|K,w）是具有一对定义（b,γ）的赋值超越扩展。假设（K(b)|K,v）是无缺陷扩展，或者f(X)是（K(X) |k,w）的关键多项式，其中f(X)是b / K的最小多项式，我们证明了扩展(K（b，X) |k (X),w）是无缺陷的。特别地，当（b,γ）是w / K的最小定义对时，扩展(K（b，X)|K(X),w）总是无缺陷的。

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引用次数: 0

On the finite generation of the cohomology of bosonizations 关于玻色子化上同调的有限生成

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-12-02 DOI: 10.1016/j.jalgebra.2025.10.057

Nicolás Andruskiewitsch , David Jaklitsch , Van C. Nguyen , Amrei Oswald , Julia Plavnik , Anne V. Shepler , Xingting Wang

We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable finite-dimensional Hopf algebras have finitely generated cohomology. In fact, our results are shown in more generality for smash products. As applications, we prove the bosonizations of some Nichols algebras (such as Nichols algebras of diagonal type, the restricted Jordan plane, Nichols algebras of direct sums of Jordan blocks plus points labeled with 1), by some suitable finite-dimensional Hopf algebras, have finitely generated cohomology, recovering some known results as well as providing new examples.

利用（Hopf）代数的变形序列，推广了Negron和Pevtsova的结果，证明了一些合适的有限维Hopf代数对一些合适的编织Hopf代数的玻色化可以有限地生成上同调。事实上，我们的结果在粉碎产品中更为普遍。作为应用，我们用合适的有限维Hopf代数证明了某些Nichols代数（如对角线型的Nichols代数、受限Jordan平面的Nichols代数、Jordan块加1标记点的直接和的Nichols代数）的玻色化有有限上同调，恢复了一些已知的结果，并提供了新的例子。

引用次数: 0

Unipotent normal subgroups of algebraic groups 代数群的幂偶正规子群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-12-02 DOI: 10.1016/j.jalgebra.2025.10.058

Damian Sercombe

Let G be an affine algebraic group scheme over a field k. We show there exists a unipotent normal subgroup of G which contains all other such subgroups; we call it the restricted unipotent radical

{Rad}_{u} (G)

of G. We investigate some properties of

{Rad}_{u} (G)

, and study those G for which

{Rad}_{u} (G)

is trivial. In particular, we relate these notions to their well-known analogues for smooth connected affine k-groups.

设G是域k上的仿射代数群方案。我们证明了G的一个单幂正规子群包含了其他所有这样的子群；我们研究了Radu(G)的一些性质，并研究了那些Radu(G)是平凡的G。特别地，我们将这些概念与光滑连接仿射k群的类似物联系起来。

引用次数: 0

On Morita equivalences with endopermutation source and isotypies 内突变源和同型的森田等价

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-12-02 DOI: 10.1016/j.jalgebra.2025.10.056

Xin Huang

We introduce a new type of equivalence between blocks of finite group algebras called an almost isotypy. An almost isotypy restricts to a weak isotypy in Broué's original definition [8, Définition 4.6], and it is slightly weaker than Linckelmann's version [17, Definition 9.5.1]. We show that a bimodule of two block algebras of finite groups - which has an endopermutation module as a source and which induces a Morita equivalence - gives rise, via slash functors, to an almost isotypy if the character values of a (hence any) source are rational integers. Consequently, if two blocks are Morita equivalent via a bimodule with endopermutation source, then they are almost isotypic. We also explain why the notion of almost isotypies is reasonable.

我们引入了有限群代数块间的一种新的等价，称为几乎同型。在brou的原始定义中，几乎同型限制为弱同型[8，d定义4.6]，比Linckelmann的版本[17，定义9.5.1]略弱。我们证明了一个有限群的两个块代数的双模——它有一个内突变模作为源并诱导了一个森田等价——如果一个（因此任何）源的字符值是有理整数，则通过斜杠函子可以产生一个几乎同型。因此，如果两个块通过具有内操作突变源的双模是森田等效的，那么它们几乎是同型的。我们还解释了为什么几乎同型的概念是合理的。

引用次数: 0

Algebraic curves with a large cyclic automorphism group 具有大循环自同构群的代数曲线

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-11-20 DOI: 10.1016/j.jalgebra.2025.11.018

Arianna Dionigi , Massimo Giulietti , Marco Timpanella

The study of algebraic curves

X

with numerous automorphisms in relation to their genus

g (X)

is a well-established area in Algebraic Geometry. In 1995, Irokawa and Sasaki [10] gave a complete classification of curves over

C

with an automorphism of order

N \geq 2 g (X) + 1

. Precisely, such curves are either hyperelliptic with

N = 2 g (X) + 2

with

g (X)

even, or are quotients of the Fermat curve of degree N by a cyclic group of order N. Such a classification does not hold in positive characteristic p, the curve with equation

y^{2} = x^{p} - x

being a well-studied counterexample. This paper successfully classifies curves with a cyclic automorphism group of order N at least

2 g (X) + 1

in positive characteristic

p \neq 2

, offering the positive characteristic counterpart to the Irokawa-Sasaki result. The possibility of wild ramification in positive characteristic has presented a few challenges to the investigation.

代数曲线X与其属g(X)有许多自同构的研究是代数几何中一个成熟的领域。1995年Irokawa和Sasaki[10]给出了C上N阶自同构≥2g(X)+1的曲线的完全分类。准确地说，这样的曲线要么是N=2g(X)+2且g(X)为偶的超椭圆曲线，要么是N次费马曲线的商，是N阶循环群。这种分类在正特征p中不成立，方程y2=xp−X的曲线是一个很好的反例。本文成功地对N阶至少为2g(X)+1且正特征p≠2的循环自同构群曲线进行了分类，给出了与Irokawa-Sasaki结果对应的正特征。阳性特征野生分枝的可能性给研究提出了一些挑战。

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引用次数: 0

Full automorphism groups of large order of compact non-orientable Riemann surfaces 大阶紧致非定向黎曼曲面的全自同构群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-11-20 DOI: 10.1016/j.jalgebra.2025.11.004

I. Anasagasti

Let X be a non-orientable Riemann surface of algebraic genus

g \geq 2

. In this paper we consider groups G of automorphisms of order greater than

12 (g - 1)

acting on such surfaces, and study whether G is the full group

Aut (X)

. The extendability of the action depends first on the NEC signature with which G acts and, in some cases, also on whether a monodromy presentation of G admits or not a particular automorphism. For each signature we study which of the two possibilities occur, and show that, whenever it does, it occurs for infinitely many values of g.

设X为代数格g≥2的不可定向黎曼曲面。本文考虑了作用于这类曲面上的大于12（G−1）阶自同构群G，并研究了G是否为Aut(X)的满群。作用的可拓性首先取决于G作用的NEC签名，在某些情况下，也取决于G的单态表示是否承认一个特定的自同构。对于每一个特征，我们研究两种可能性中的哪一种会发生，并表明，无论何时发生，它都会对无穷多个g值发生。

引用次数: 0

Whittaker supermodules over the super Schrödinger algebra 超Schrödinger代数上的Whittaker超模

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-11-20 DOI: 10.1016/j.jalgebra.2025.11.012

Xinyue Wang , Liangyun Chen , Yao Ma

In this paper, let

S

denote the

N = 1

super Schrödinger algebra in

(1 + 1)

-dimensional spacetime, and

U (S)

the universal enveloping algebra of

S

. We first introduce the notion of Ore extension in the context of super ring. As an application, we use Ore extension to find the tensor product decomposition of the localization of

U (S)

at the powers of the element G, which gives the Casimir element and center of

U (S)

. Then we define the Whittaker

S

-supermodules, and classify the simple Whittaker

S

-supermodules at zero level and nonzero level, respectively. In particular, Whittaker supermodules over

osp (1 | 2)

are constructed and classified.

本文设S为（1+1）维时空中N=1的超Schrödinger代数，U(S)为S的全称包络代数。我们首先在超环的背景下引入了oreextension的概念。作为应用，我们利用Ore扩展求出U(S)在元素G的幂次处的局域的张量积分解，得到U(S)的卡西米尔元素和中心。然后定义了Whittaker s -超模，并分别对零水平和非零水平的简单Whittaker s -超模进行了分类。特别地，构造并分类了osp（1 bb0 2）上的Whittaker超模。

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引用次数: 0

On character values of GLn(Fq) GLn（Fq）的特征值

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-11-20 DOI: 10.1016/j.jalgebra.2025.10.052

Naihuan Jing , Yu Wu

In this paper, we use vertex operator techniques to compute character values on unipotent classes of

{GL}_{n} (F_{q})

. By realizing the Grothendieck ring

R_{G} = ⨁_{n \geq 0}^{\infty} R ({GL}_{n} (F_{q}))

as Fock spaces, we formulate the Murnaghan-Nakayama rule of

{GL}_{n} (F_{q})

between Schur functions colored by an orbit ϕ of linear characters of

{\overline{F}}_{q}

and another orbit of modified Hall-Littlewood functions colored by

f_{1} = t - 1

under the Frobenius automorphisms. Our formulation of character values using vertex operators offers a practical approach for computing special values at unipotent classes for

{GL}_{n} (F_{q})

. As an application, these vertex-algebraic techniques allow us to derive the Steinberg characters of

{GL}_{n} (F_{q})

, results that were previously obtained by Curtis, Lehrer, and Tits through the geometry of homology groups of spherical buildings, and by Springer and Zelevinsky via the theory of Hopf algebras.

在本文中，我们使用顶点算子技术来计算GLn（Fq）的幂偶类上的特征值。通过实现Grothendieck环RG= n≥0∞R（GLn(Fq)）作为Fock空间，我们在Frobenius自同构下，在由F的线性特征的一个轨道φ所染色的Schur函数和由f1=t−1所染色的另一个修正的Hall-Littlewood函数的轨道之间，建立了GLn（Fq）的Murnaghan-Nakayama规则。我们使用顶点运算符的字符值公式为计算GLn（Fq）的无效类的特殊值提供了一种实用的方法。作为一种应用，这些顶点代数技术使我们能够推导出GLn（Fq）的Steinberg特征，这些结果之前由Curtis， Lehrer和Tits通过球形建筑的同调群的几何以及施普林格和Zelevinsky通过Hopf代数理论获得。

引用次数: 0

Additive and multiplicative coinvariant spaces of Weyl groups in the light of harmonics and graded transfer Weyl群的加性和乘性协不变空间

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-11-20 DOI: 10.1016/j.jalgebra.2025.11.008

Sebastian Debus , Tobias Metzlaff

The action of a Weyl group on the associated weight lattice induces an additive action on the symmetric algebra and a multiplicative action on the group algebra of the lattice. We show that the coinvariant space of the multiplicative action affords the regular representation and is isomorphic to a space of multiplicative harmonics, which corresponds to existing results for additive coinvariants of reflection groups. We then design an algorithm to compute a multiplicative coinvariant basis from an additive one. The algorithm preserves isotypic decomposition and graded structure and enables the study of multiplicative coinvariants by integrating combinatorial knowledge from the additive setting. We investigate the Weyl groups of type A and C to find new explicit equivariant maps and combinatorial structure.

Weyl群对关联权格的作用在对称代数上引起加性作用，在格的群代数上引起乘性作用。我们证明了乘法作用的协不变空间具有正则表示，并同构于一个乘法谐波空间，这与已有的关于反射群的加性协不变的结果相对应。然后，我们设计了一种算法，从一个加性基计算一个乘性协不变基。该算法保留了同型分解和梯度结构，并通过集成来自加性设置的组合知识来研究乘法协变量。我们研究了A型和C型的Weyl群，找到了新的显式等变映射和组合结构。

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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

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Journal of Algebra

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