Journal of Pure and Applied Algebra最新文献

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Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories 相干剪切范畴的无扭类及其塞尔子范畴的分类

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-05 DOI: 10.1016/j.jpaa.2024.107799

Shunya Saito

In this paper, we classify several subcategories of the category of coherent sheaves on a divisorial noetherian scheme (e.g. a quasi-projective scheme over a commutative noetherian ring). More precisely, we classify the torsionfree (resp. torsion) classes closed under tensoring with line bundles by the subsets (resp. specialization-closed subsets) of the scheme, which generalizes the classification of torsionfree (resp. torsion) classes of the category of finitely generated modules over a commutative noetherian ring by Takahashi (resp. Stanley–Wang).

Furthermore, we classify the Serre subcategories of a torsionfree class (in the sense of Quillen's exact categories) by using the above classifications, which gives a certain generalization of Gabriel's classification of Serre subcategories. As explicit applications, we classify the Serre subcategories of the category of maximal pure sheaves, which are a natural generalization of vector bundles for reducible schemes, on a reduced projective curve over a field, and the category of maximal Cohen-Macaulay modules over a one-dimensional Cohen-Macaulay ring.

在本文中，我们对可分诺特方案（例如交换诺特环上的准投影方案）上的相干剪切类别的几个子类别进行了分类。更确切地说，我们用方案的子集（或特化封闭子集）来分类在线束张弦下封闭的无扭（或有扭）类，这概括了高桥（Takahashi）（或 Stanley-Wang）对交换诺特环上有限生成模块范畴的无扭（或有扭）类的分类。此外，我们还利用上述分类法对无扭类（在奎伦精确范畴的意义上）的塞雷子范畴进行了分类，这是对加布里埃尔的塞雷子范畴分类法的某种概括。作为明确的应用，我们对最大纯剪范畴的塞雷子范畴和一维科恩-麦考莱环上的最大科恩-麦考莱模块范畴进行了分类，前者是对可还原方案的向量束的自然概括，后者是对一个域上的还原投影曲线的自然概括。

引用次数: 0

On the Drinfeld double of the restricted Jordan plane in characteristic 2 论特征 2 中受限约旦平面的德林费尔德双倍性

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-05 DOI: 10.1016/j.jpaa.2024.107798

Nicolás Andruskiewitsch , Dirceu Bagio , Saradia Della Flora , Daiana Flôres

We consider the restricted Jordan plane in characteristic 2, a finite-dimensional Nichols algebra quotient of the Jordan plane that was introduced by Cibils, Lauve and Witherspoon. We extend results from arXiv:2002.02514 on the analogous object in odd characteristic. We show that the Drinfeld double of the restricted Jordan plane fits into an exact sequence of Hopf algebras whose kernel is a normal local commutative Hopf subalgebra and the cokernel is the restricted enveloping algebra of a restricted Lie algebra $m$ of dimension 5. We show that $u (m)$ is tame and compute explicitly the indecomposable modules. An infinite-dimensional Hopf algebra covering the Drinfeld double of the restricted Jordan plane is introduced. Various quantum Frobenius maps are described.

我们考虑的是特征 2 中的受限约旦平面，它是由 Cibils、Lauve 和 Witherspoon 引入的约旦平面的有限维尼科尔斯代数商。我们扩展了 arXiv:2002.02514 中关于奇特征中类似对象的结果。我们证明，受限乔丹平面的德林费尔德双重符合霍普夫代数的精确序列，其内核是正常局部交换霍普夫子代数，而协核是维数为 5 的受限列代数 m 的受限包络代数。我们证明 u(m) 是驯服的，并明确计算了不可分解模块。我们引入了一个覆盖受限约旦平面的德林菲尔德双的无穷维霍普夫代数。描述了各种量子弗罗贝尼斯映射。

引用次数: 0

The classification of automorphisms and quotients of Calabi-Yau threefolds of type A A 型 Calabi-Yau 三折的自形和商的分类

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-30 DOI: 10.1016/j.jpaa.2024.107796

Martina Monti

The aim of the paper is to investigate the only two families $F_{G}^{A}$ of Calabi-Yau 3-folds $A / G$ with A an abelian 3-fold and $G \leq Aut (A)$ a finite group acting freely: one is constructed in [11] and the other is presented here. We provide a complete classification of the automorphism group of $X \in F_{G}^{A}$ . Additionally, we construct and classify the quotients $X / ϒ$ for any $ϒ \leq Aut (X)$ . Specifically, for those groups ϒ that preserve the volume form of X then $X / ϒ$ admits a desingularization Y which is a Calabi-Yau 3-fold: we compute the Hodge numbers and the fundamental group of these Y, thereby determining all topological in-equivalent Calabi-Yau 3-folds obtained in this way.

本文旨在研究 Calabi-Yau 3 折叠体中仅有的两个具有无常 3 折叠体和自由作用有限群的系列：一个是在《......》中构建的，另一个是在本文中提出的。我们提供了.的自变群的完整分类。此外，我们还构造并分类了任意.的商。具体地说，对于那些保留其体积形式的群ϒ，我们会给出一个卡拉比优 3 折叠的去奇化：我们计算了这些群的霍奇数和基群，从而确定了以这种方式得到的所有拓扑内等价卡拉比优 3 折叠。

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引用次数: 0

Self-injective algebras under derived equivalences 派生等价下的自注入代数

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-30 DOI: 10.1016/j.jpaa.2024.107795

Changchang Xi , Jin Zhang

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences.

两个派生等价、自射阿廷代数的中山排列是共轭的。本文给出了一种不同但基本的方法，以证明任意域上的有限维代数的弱对称性和自射性在派生等价条件下得以保留。

引用次数: 0

Filtered colimit elimination from Birkhoff's variety theorem 从伯克霍夫品种定理出发的过滤式消顶法

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-28 DOI: 10.1016/j.jpaa.2024.107794

Yuto Kawase

Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem, closure under filtered colimits is required. However, in some special cases, such as finite-sorted equational theories and ordered algebraic theories, the theorem holds without assuming closure under filtered colimits. We call this phenomenon “filtered colimit elimination,” and study a sufficient condition for it. We show that if a locally finitely presentable category $A$ satisfies a noetherian-like condition, then filtered colimit elimination holds in the generalized Birkhoff's theorem for algebras relative to $A$ .

伯克霍夫综类定理是普遍代数的基本定理，它断言，当且仅当给定代数的一个子类满足特定的闭包性质时，它是可以用方程定义的。在该定理的广义版本中，要求在滤波夹层下闭合。然而，在某些特殊情况下，比如有限排序方程理论和有序代数理论，无需假设在过滤式收敛下的封闭性，该定理也是成立的。我们称这种现象为 "过滤式顶点消除"，并研究了它的充分条件。我们证明，如果一个局部有限可呈现范畴 A 满足一个类似于诺特的条件，那么在相对于 A 的代数代数的广义伯克霍夫定理中，过滤式顶点消除成立。

引用次数: 0

On p-parts of character degrees 关于字符度的 p 部分

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-22 DOI: 10.1016/j.jpaa.2024.107793

Guohua Qian

Let G be a finite group and p be a prime. In this paper, we get the sharp bound for $| G / O_{p} (G) |_{p}$ under the assumption that either $p^{2} ∤ χ (1)$ for all $χ \in Irr (G)$ or $p^{2} ∤ ϕ (1)$ for all $ϕ \in {IBr}_{p} (G)$ . This would settle two conjectures raised by Lewis, Navarro, Tiep, and Tong-Viet in [7].

设 G 是有限群，p 是素数。本文假设所有 χ∈Irr(G) 均为 p2∤χ(1)，或所有 ϕ∈IBrp(G) 均为 p2∤j(1)，从而得到 |G/Op(G)|p 的锐界。这将解决 Lewis、Navarro、Tiep 和 Tong-Viet 在 [7] 中提出的两个猜想。

引用次数: 0

Corrigendum to “Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products” [J. Pure Appl. Algebra 225 (2021) 106597] 一般扭曲张量乘的霍希契尔德同调上的格尔斯滕哈伯括号" [J. Pure Appl. Algebra 225 (2021) 106597] 更正

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-21 DOI: 10.1016/j.jpaa.2024.107788

T. Karadag , D. McPhate , P.S. Ocal , T. Oke , S. Witherspoon

In our paper [1], several maps in Section 4 were incorrect. We correct them here. This oversight does not affect any of the results in the paper.

在我们的论文[1]中，第 4 节中的几个地图是不正确的。我们在此予以更正。这一疏忽不会影响论文中的任何结果。

引用次数: 0

On the Auslander–Bridger–Yoshino theory for complexes of finitely generated projective modules 关于有限生成的射影模块复数的奥斯兰德-布里奇-吉野理论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-10 DOI: 10.1016/j.jpaa.2024.107790

Yuya Otake

Let R be a two-sided noetherian ring. Auslander and Bridger developed a theory of projective stabilization of the category of finitely generated R-modules, which is called the stable module theory. Recently, Yoshino established a stable “complex” theory, i.e., a theory of a certain stabilization of the homotopy category of complexes of finitely generated projective R-modules. We introduce higher versions of several notions introduced by Yoshino, such as ^⁎torsionfreeness and ^⁎reflexivity. Also, we prove the Auslander–Bridger approximation theorem for complexes of finitely generated projective R-modules.

设 R 是一个双面诺特环。Auslander 和 Bridger 提出了有限生成的 R 模范畴的投影稳定理论，称为稳定模理论。最近，吉野建立了稳定 "复数 "理论，即有限生成的射影 R 模块的复数同调范畴的某种稳定理论。我们引入了吉野引入的几个概念的更高版本，如⁎无扭转性和⁎反身性。此外，我们还证明了有限生成的投影 R 模块复数的奥斯兰德-布里奇近似定理。

引用次数: 0

Exotic fusion system on a subgroup of the monster 怪物子群上的奇异融合系统

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-08 DOI: 10.1016/j.jpaa.2024.107792

Patrick Serwene

We prove that an exotic fusion system described by Grazian on a subgroup of the Monster group is block-exotic, thus proving that exotic and block-exotic fusion systems are the same for all p-groups with sectional rank 3, where $p \geq 5$ .

我们证明了格拉兹安在怪兽群的一个子群上描述的异域融合系统是块状异域融合系统，从而证明了异域融合系统和块状异域融合系统对于所有截面秩为 3 的-群都是一样的，其中 .

引用次数: 0

On the structures of a monoid of triangular vector-permutation polynomials, its group of units and its induced group of permutations 论三角形向量置换多项式单元的结构、其单位群和诱导置换群

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-08-08 DOI: 10.1016/j.jpaa.2024.107789

Amr Ali Abdulkader Al-Maktry

<div>Let <math><mi>n</mi><mo>></mo><mn>1</mn></math> and let R be a commutative ring with identity <math><mn>1</mn><mo>≠</mo><mn>0</mn></math> and <math><mi>R</mi><msup><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math> the set of all n-tuples of polynomials of the form <math><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math>, where <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∈</mo><mi>R</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math>. We call these n-tuples vector-polynomials. We define composition on <math><mi>R</mi><msup><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math> by<math><mover><mrow><mi>g</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>∘</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>,</mo><mtext> where </mtext><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>,</mo><mover><mrow><mi>g</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>.</mo></math> In this paper, we investigate vector-polynomials of the form<math><mover><mrow><mi>f</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><m

让和是一个交换环，它具有同一性和所有形式为 , 的多项式的-元组的集合。我们称这些元组为向量多项式。在本文中，我们将研究形式为的向量多项式，其中对和的元素进行置换，使得每个元素都映射到（）的单元中。我们证明，每一个这样的向量多项式都会对和的元素进行置换，并且所有这样的向量多项式的集合都是一个关于组成的单项式。我们还证明，当且仅当是的-自同构时，在是可逆的。此外，我们将单项式分解为单项式的迭代半直积。通过这样的分解，我们可以得到类似的单位群分解，当有限时，也可以得到类似的诱导排列群分解。此外，诱导群的分解还有助于我们描述它的某些性质。

引用次数: 0

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