Journal of Algebra最新文献

英文中文

On the Hopf envelope of finite-dimensional bialgebras 有限维双代数的Hopf包络

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-15 Epub Date: 2026-01-07 DOI: 10.1016/j.jalgebra.2025.12.022

Alessandro Ardizzoni , Claudia Menini , Paolo Saracco

The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf algebra theory, but their construction is not particularly handy or friendly. In this note, we offer a novel realisation of the Hopf envelope and of the cofree Hopf algebra of a finite-dimensional bialgebra as a particular quotient and sub-bialgebra, respectively, of the bialgebra itself. Our construction can also be extended to the infinite-dimensional case, provided that the bialgebra satisfies additional conditions, such as being right perfect as an algebra or admitting a n-antipode, the latter being a notion hereby introduced. Remarkably, the machinery we develop also allows us to give a new description of the Hopf envelope of a commutative bialgebra and of the cofree cocommutative Hopf algebra of a cocommutative bialgebra.

双代数的霍普夫包络是由给定双代数生成的自由霍普夫代数。在Hopf代数理论中，它的存在性和共自由Hopf代数的存在性是一个众所周知的事实，但它们的构造不是特别方便或友好。在这篇文章中，我们提供了一种新的实现，将有限维双代数的Hopf包络和协无Hopf代数分别作为双代数本身的一个特殊商和子双代数。我们的构造也可以推广到无限维的情况，只要这个双代数满足附加条件，如作为一个代数是正确完备的，或者承认一个n对跖，后者是这里引入的一个概念。值得注意的是，我们开发的机制还允许我们给出可交换双代数的Hopf包络和可交换双代数的无协交换Hopf代数的新描述。

引用次数: 0

Almost inner derivations of Lie superalgebras 李超代数的几乎内导

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-15 Epub Date: 2025-12-08 DOI: 10.1016/j.jalgebra.2025.11.030

Vera Serganova , Arkady Vaintrob

An almost inner derivation of a Lie algebra L is a derivation that coincides with an inner derivation on each one-dimensional subspace of L. The almost inner derivations form a subalgebra

aDer (L)

of the Lie algebra

Der (L)

of all derivations of L, containing the inner derivations

iDer (L)

as an ideal. If L is a simple finite-dimensional Lie algebra, then

aDer (L) = iDer (L)

, since all derivations of L are inner.

In this paper, we introduce and study almost inner derivations of Lie superalgebras. Since simple Lie superalgebras may admit non-inner outer derivations, the existence of non-inner almost inner derivations becomes a nontrivial question. Nevertheless, we show that all almost inner derivations of finite-dimensional simple Lie superalgebras over

C

are inner. We also give examples of naturally occurring non-inner almost inner derivations of some quasireductive Lie superalgebras related to the Sato-Kimura classification of prehomogeneous vector spaces.

李代数L的几乎内导数是与L的每一一维子空间上的内导数相吻合的导数。几乎内导数构成了L的所有导数的李代数Der(L)的子代数aDer(L)，其中包含了作为理想的内导数iDer(L)。如果L是一个简单的有限维李代数，则aDer(L)=iDer(L)，因为L的所有导都是内导。本文引入并研究了李超代数的几乎内导。由于简单李超代数可以允许非内外导，因此非内几乎内导的存在性成为一个非平凡问题。然而，我们证明了C上有限维简单李超代数的所有几乎内导都是内导。我们还给出了与预齐次向量空间的Sato-Kimura分类有关的一些拟约李超代数的自然非内几乎内导数的例子。

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引用次数: 0

The first Brauer-Thrall conjecture for extriangulated length categories 外三角化长度范畴的第一个Brauer-Thrall猜想

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-15 Epub Date: 2025-12-12 DOI: 10.1016/j.jalgebra.2025.12.014

Li Wang , Jiaqun Wei

Let

(A, Θ)

be an extriangulated length category. We introduce the notation of Gabriel-Roiter measure with respect to Θ and extend Gabriel's main property to this setting. Using this measure, when

(A, Θ)

satisfies some reasonable conditions, we prove that

A

has an infinite number of pairwise nonisomorphic indecomposable objects if and only if it has indecomposable objects of arbitrarily large length. That is, the first Brauer-Thrall conjecture holds.

设（A，Θ）是一个外三角化的长度范畴。我们引入关于Θ的加布里埃尔-罗伊特测度的符号，并将加布里埃尔的主要性质扩展到这个设置。利用这一测度，当（A，Θ）满足某些合理条件时，我们证明了当且仅当A具有任意大长度的不可分解对象时，A具有无限个对非同构不可分解对象。也就是说，第一个Brauer-Thrall猜想成立。

引用次数: 0

Local–global generation property of commutators in finite π-soluble groups 有限π可溶群中换向子的局部-全局生成性质

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-15 Epub Date: 2026-01-06 DOI: 10.1016/j.jalgebra.2025.12.020

Cristina Acciarri , Robert M. Guralnick , Evgeny Khukhro , Pavel Shumyatsky

For a group A acting by automorphisms on a group G, let

I_{G} (A)

denote the set of commutators

[g, a] = g^{- 1} g^{a}

, where

g \in G

and

a \in A

, so that

[G, A]

is the subgroup generated by

I_{G} (A)

. We prove that if A is a π-group of automorphisms of a π-soluble finite group G such that any subset of

I_{G} (A)

generates a subgroup that can be generated by r elements, then the rank of

[G, A]

is bounded in terms of r. Examples show that such a result does not hold without the assumption of π-solubility. Earlier we obtained this type of results for groups of coprime automorphisms and for Sylow p-subgroups of p-soluble groups.

对于由自同构作用于群G的群a，令IG(a)表示对易子集合[G， a]= G−1ga，其中G∈G，a∈a，使得[G， a]是由IG(a)生成的子群。证明了如果A是π可溶有限群G的自同构π群，使得IG(A)的任意子集都能生成一个可由r个元素生成的子群，则[G，A]的秩是用r有界的。实例表明，如果没有π可溶性的假设，这个结果是成立的。在此之前，我们得到了同素自同构群和p可溶群的Sylow p亚群的这类结果。

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引用次数: 0

The Hilbert scheme component of the schematic union of two conics 两个二次曲线的图解并集的希尔伯特格式分量

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-15 Epub Date: 2025-12-05 DOI: 10.1016/j.jalgebra.2025.12.004

Jacqueline Rojas , Adriana Silva , Fernando Xavier

Here we construct an explicit parameter space for the 16–dimensional component

H

of the Hilbert's scheme

{Hilb}^{4 t + 2} P^{3}

whose generic point is the schematic union of two conics. As an application, we compute the degree of the locus of surfaces of degree

d \geq 5

P^{3}

, containing the schematic union of two conics.

本文构造了Hilbert格式Hilb4t+2P3的16维分量H的显式参数空间，其一般点为两个二次曲线的图解并。作为应用，我们计算了包含两个二次曲线的图解并集的P3中d≥5次曲面轨迹的度。

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 : 2026-04-01 Epub 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 : 2026-04-01 Epub 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

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 : 2026-04-01 Epub 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

Categorical representation of DRC-semigroups drc -半群的分类表示

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-11-20 DOI: 10.1016/j.jalgebra.2025.11.006

James East , Matthias Fresacher , P.A. Azeef Muhammed , Timothy Stokes

DRC-semigroups model associative systems with domain and range operations, and contain many important classes, such as inverse, restriction, Ehresmann, regular ⁎-, and ⁎-regular semigroups; concrete examples include diagram monoids, linear monoids, relation monoids, among many others. In this paper we show that the category of DRC-semigroups is isomorphic to a category of certain biordered categories whose object sets are projection algebras in the sense of Jones. This extends the recent groupoid approach to regular ⁎-semigroups of the first and third authors. We also establish the existence of free DRC-semigroups by constructing a left adjoint to the forgetful functor into the category of projection algebras.

dc -半群用域和值域运算对关联系统进行建模，并包含了许多重要的类，如逆半群、限制半群、Ehresmann半群、正则半群和正则半群；具体的例子包括图一元群、线性一元群、关系一元群等。本文证明了dc -半群的范畴与某些双序范畴的范畴同构，这些双序范畴的对象集是Jones意义上的投影代数。这将最近的类群方法扩展到第一和第三作者的正则半群。通过构造投影代数范畴中遗忘函子的左伴随，证明了自由dc -半群的存在性。

引用次数: 0

Linear characters for p-basic groups p基群的线性特征

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-12-04 DOI: 10.1016/j.jalgebra.2025.11.027

Alexandre Turull

In a recent paper, Turull showed that associated with any p-block B with cyclic defect group of any finite group are two linear characters. These two linear characters allow us to calculate easily the Hasse invariant of the characters of B. A different method to describe these Hasse invariant was proved by Nebe. In a different paper, Turull showed that the Hasse invariant of any irreducible character of a finite group G can be calculated from the Hasse invariant of the p-basic groups. In the present paper, we describe the two linear characters associated with any of the relevant characters of the p-basic groups, and we obtain in this way their Hasse invariants as well. The formulas are based on a single exceptional character of B and are fairly straightforward and uniform.

在最近的一篇论文中，Turull证明了与任意有限群的循环缺陷群的任意p块B相关联的是两个线性特征。这两个线性特征使我们可以很容易地计算出b的特征的Hasse不变量，Nebe证明了描述这些Hasse不变量的不同方法。在另一篇论文中，Turull证明了有限群G的任意不可约特征的Hasse不变量可以由p基群的Hasse不变量计算出来。在本文中，我们描述了与p基群的任何相关特征相关联的两个线性特征，并由此得到了它们的Hasse不变量。这些公式基于B的一个例外字符，相当简单和统一。

引用次数: 0

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