Journal of Algebra最新文献

英文中文

Tan's conjecture on irregular family over P1 Tan关于P1上不规则族的猜想

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.2025.12.005

Xin Lü , Peng Sun

Let

f : S \to P^{1}

be a non-trivial semi-stable fibration of genus

g \geq 2

with s singular fibers over the complex numbers. Tan conjectured that

s \geq 6

g ≫ 0

. We study this conjecture for irregular surfaces. More precisely, we prove that

s \geq 6

if the irregularity

q (S) \geq 2

设f:S→P1为g≥2属的非平凡半稳定纤维，其复数上有S个奇异纤维。Tan推测，如果g≠0，则s≥6。我们研究了不规则曲面的这个猜想。更准确地说，我们证明如果不规则性q(s)≥2，则s≥6。

引用次数: 0

Multiple rational normal forms in Lie theory 李论中的多重有理范式

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-12-05 DOI: 10.1016/j.jalgebra.2025.11.019

Dmitriy Voloshyn

We study the decomposition of a generic element

g \in G

of a connected reductive complex algebraic group G in the form

g = N (g) B (g) \bar{u} N {(g)}^{- 1}

where

N : G ⇢ N_{-}

and

B : G ⇢ B_{+}

are rational maps onto a unipotent subgroup

N_{-}

and a Borel subgroup

B_{+}

opposite to

N_{-}

, and

\bar{u}

is a representative of a Weyl group element u. We introduce a class of rational Weyl group elements that give rise to such decompositions, and study their various properties.

研究了连通约化复代数群g的一般元素g∈g的分解，其形式为g=N(g)B(g)u¯N(g)−1，其中N: g讲解N−和B: g讲解B+是幂偶子群N−和与N−相对的Borel子群B+的有理映射，u¯是Weyl群元素u的代表。我们引入了一类引起这种分解的有理Weyl群元素，并研究了它们的各种性质。

引用次数: 0

On the Dong Property for a binary quadratic operad 二元二次运算的Dong性质

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.2025.11.025

P.S. Kolesnikov , B.K. Sartayev

The classical Dong Lemma for distributions over a Lie algebra lies in the foundation of the theory of vertex and conformal algebras. In this paper, we find necessary and sufficient condition for a variety of nonassociative algebras with binary operations to satisfy the analogue of the Dong Lemma. In particular, it turns out that for alternative, Novikov, and Novikov–Poisson algebras the Dong Lemma holds true. The criterion is stated in the language of operads, so we determine for which binary quadratic operads the Dong Lemma holds in the corresponding class of algebras. As an application, we show the black Manin product of such Dong operads is also a Dong operad.

李代数上分布的经典董引理是顶点代数和共形代数理论的基础。本文给出了一类具有二元运算的非结合代数满足类似董引理的充分必要条件。特别地，对于可选代数，Novikov代数和Novikov - poisson代数，Dong引理是成立的。该判据是用操作数的语言表述的，因此我们确定了董引理在相应的代数类中对哪些二元二次操作数成立。作为一种应用，我们证明了这些侗族算子的黑曼宁产物也是侗族算子。

引用次数: 0

On subalgebras of the Griess algebra with alternating Miyamoto group 交替Miyamoto群的Griess代数的子代数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-12-05 DOI: 10.1016/j.jalgebra.2025.11.032

Clara Franchi , Mario Mainardis

We use Majorana representations to study the subalgebras of the Griess algebra that have shape

(2 B, 3 A, 5 A)

and whose associated Miyamoto groups are isomorphic to

A_{n}

. We prove that these subalgebras exist only if

n \in {5, 6, 8}

. The case

n = 5

was already treated by Ivanov, Seress, McInroy, and Shpectorov. In case

n = 6

we prove that these algebras are all isomorphic and provide their precise description. In case

n = 8

we prove that these algebras do not arise from standard Majorana representations.

我们用Majorana表示研究了形状为（2B,3A,5A）的Griess代数的子代数，其相关的Miyamoto群与An同构。证明这些子代数仅在n∈{5,6,8}时存在。病例n=5已经由Ivanov、Seress、McInroy和Shpectorov治疗过。在n=6的情况下，我们证明了这些代数都是同构的，并给出了它们的精确描述。在n=8的情况下，我们证明了这些代数不是由标准马约拉纳表示产生的。

引用次数: 0

Solution of a problem in monoidal categorification by additive categorification 用加性分类法求解一元分类问题

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.2025.11.017

Alessandro Contu

In 2021, Kashiwara–Kim–Oh–Park constructed cluster algebra structures on the Grothendieck rings of certain monoidal subcategories of the category of finite-dimensional representations of a quantum loop algebra, generalizing Hernandez–Leclerc's pioneering work from 2010. They stated the problem of finding explicit quivers for the seeds they used. We provide a solution by using Palu's generalized mutation rule applied to the cluster categories associated with certain algebras of global dimension at most 2, for example tensor products of path algebras of representation-finite quivers. Thus, our method is based on (and contributes to) the bridge, provided by cluster combinatorics, between the representation theory of quantum groups and that of quivers with relations.

2021年，Kashiwara-Kim-Oh-Park在量子环代数有限维表示范畴的某些单面子范畴的Grothendieck环上构建了簇代数结构，推广了Hernandez-Leclerc在2010年的开创性工作。他们提出了为他们使用的种子找到明确的震颤的问题。本文利用帕鲁广义突变规则，给出了与全局维数不超过2的代数相关的聚类范畴的一个解，例如表示有限振子路径代数的张量积。因此，我们的方法是基于（并有助于）在量子群的表示理论和带关系的颤振的表示理论之间由簇组合提供的桥梁。

引用次数: 0

A proof of the Naito–Sagaki conjecture via the branching rule for ıquantum groups 用ıquantum群的分支规则证明奈东-佐垣猜想

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-11-15 DOI: 10.1016/j.jalgebra.2025.10.049

Satoshi Naito , Yujin Suzuki , Hideya Watanabe

The Naito–Sagaki conjecture asserts that the branching rule for the restriction of finite-dimensional, irreducible polynomial representations of

G L_{2 n} (C)

S p_{2 n} (C)

amounts to the enumeration of certain “rational paths” satisfying specific conditions. This conjecture can be thought of as a non-Levi type analog of the Levi type branching rule, stated in terms of the path model due to Littelmann, and was proved combinatorially in 2018 by Schumann–Torres. In this paper, we give a new proof of the Naito–Sagaki conjecture independently of Schumann–Torres, using the branching rule based on the crystal basis theory for ıquantum groups of type

A {II}_{2 n - 1}

. Here, note that ıquantum groups are certain coideal subalgebras of a quantized universal enveloping algebra obtained by q-deforming symmetric pairs, and also regarded as a generalization of quantized universal enveloping algebras; these were defined by Letzter in 1999, and since then their representation theory has become an active area of research. The main ingredients of our approach are certain combinatorial operations, such as promotion operators and Kashiwara operators, which are well-suited to the representation theory of complex semisimple Lie algebras.

Naito-Sagaki猜想断言限制GL2n(C)到Sp2n(C)的有限维、不可约多项式表示的分支规则等于满足特定条件的某些“有理路径”的枚举。这个猜想可以被认为是Levi型分支规则的非Levi型模拟，用Littelmann的路径模型来表述，并在2018年由Schumann-Torres组合证明。本文利用基于晶体基理论的分支规则，对AII2n−1型ıquantum群给出了独立于Schumann-Torres的Naito-Sagaki猜想的一个新的证明。在这里，注意ıquantum群是由q-变形对称对得到的量子化泛包络代数的某些共理想子代数，也被视为量子化泛包络代数的推广；这是Letzter在1999年定义的，从那时起，他们的表征理论就成为了一个活跃的研究领域。我们的方法的主要成分是某些组合运算，如提升算子和Kashiwara算子，它们非常适合于复半单李代数的表示理论。

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引用次数: 0

Isogenies and congruence subgroups 同基因和同余子群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-04-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jalgebra.2025.12.001

Shengkai Mao

Let

π : G \to H

be an isogeny between linear algebraic groups over a number field E, S be a finite set of places of E. In this note, we give some criteria for when a S-congruence subgroup of

G (E)

has S-congruence image in

H (E)

following [7].

设π:G→H是数域E上的线性代数群之间的等同子群，S是E的有限位集，本文给出了G(E)的S同余子群在H(E)上有S同余像的几个判据。

引用次数: 0

Refined Kac polynomials for quivers with enough loops 具有足够环的颤振的改进Kac多项式

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.2025.10.054

Jiuzhao Hua

Kac's conjecture, now a theorem, asserts that the polynomial which counts the isomorphism classes of absolutely indecomposable representations of a quiver over a finite field, for any given dimension vector, has only non-negative integer coefficients. In this paper, we provide a refinement of the Kac polynomial for quivers with enough loops, expressing it as a sum of refined Kac polynomials indexed by tuples of partitions. These refined polynomials also have non-negative integer coefficients. We conclude by suggesting several avenues for future research.

Kac的猜想，现在是一个定理，断言在有限域上，对于任何给定的维向量，计算一个颤振绝对不可分解表示的同构类的多项式，只有非负整数系数。在本文中，我们对具有足够环的颤振给出了Kac多项式的一个改进，将其表示为由分区元组索引的改进Kac多项式的和。这些精细多项式也有非负整数系数。最后，我们提出了未来研究的几个途径。

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 : 2026-04-01 Epub 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

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 : 2026-04-01 Epub 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

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