Journal of Pure and Applied Algebra最新文献

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On the cohomology of Lie algebras associated with graphs 论与图相关的李代数同调

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-11-14 DOI: 10.1016/j.jpaa.2024.107838

Marco Aldi , Andrew Butler , Jordan Gardiner , Daniele Grandini , Monica Lichtenwalner , Kevin Pan

We describe a canonical decomposition of the cohomology of the Dani-Mainkar 2-step nilpotent Lie algebras associated with graphs. As applications, we obtain explicit formulas for the third cohomology of any Dani-Mainkar Lie algebra and for the cohomology in all degrees of Lie algebras associated with arbitrary star graphs. We also describe a procedure to reduce the calculation of the cohomology of solvable Lie algebras associated with graphs through the Grantcharov-Grantcharov-Iliev construction to the cohomology of Dani-Mainkar Lie algebras.

我们描述了与图相关的丹尼-马恩卡 2 阶零能烈代数的同调的规范分解。作为应用，我们得到了任何 Dani-Mainkar Lie 代数的第三同调的明确公式，以及与任意星形图相关的 Lie 代数的所有度数的同调的明确公式。我们还描述了通过格兰查洛夫-格兰查洛夫-伊利耶夫构造将与图相关的可解李代数的同调计算简化为丹尼-马恩卡尔李代数的同调计算的过程。

引用次数: 0

Normalizer quotients of symmetric groups and inner holomorphs 对称群的归一化商与内全形

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-11-13 DOI: 10.1016/j.jpaa.2024.107839

Alexei Entin , Cindy (Sin Yi) Tsang

We show that every finite group T is isomorphic to a normalizer quotient

N_{S_{n}} (H) / H

for some n and a subgroup

H \leq S_{n}

. We show that this holds for all large enough

n \geq n_{0} (T)

and also with

S_{n}

replaced by

A_{n}

. The two main ingredients in the proof are a recent construction due to Cornulier and Sambale of a finite group G with

Out (G) ≅ T

(for any given finite group T) and the determination of the normalizer in

Sym (G)

of the inner holomorph

InHol (G) \leq Sym (G)

for any centerless indecomposable finite group G, which may be of independent interest.

我们证明，对于某个 n 和一个子群 H≤Sn 而言，每个有限群 T 都与一个归一化商 NSn(H)/H 同构。我们证明，对于所有足够大的 n≥n0(T)，以及用 An 代替 Sn 时，这一点都成立。证明的两个主要因素是 Cornulier 和 Sambale 最近构建的一个有限群 G 的 Out(G)≅T（对于任意给定的有限群 T），以及对于任意无中心不可分解有限群 G 的内全形 InHol(G)≤Sym(G)在 Sym(G)中的归一化子的确定，这两个因素可能会引起独立的兴趣。

引用次数: 0

Laumon parahoric local models via quiver Grassmannians 通过四维格拉斯曼的劳蒙准局部模型

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-11-05 DOI: 10.1016/j.jpaa.2024.107837

Evgeny Feigin , Martina Lanini , Alexander Pütz

Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers are quiver Grassmannians for the loop quiver and the special fiber is a certain quiver Grassmannian for the cyclic quiver. The whole family sits inside the Gaitsgory central degeneration of the affine Grassmannians. We study the properties of the special fibers of the (complex) Laumon local models for arbitrary parahoric subgroups in type A using the machinery of quiver representations. We describe the irreducible components and the natural strata with respect to the group action for the quiver Grassmannians in question. We also construct a cellular decomposition and provide an explicit description for the corresponding poset of cells. Finally, we study the properties of the desingularizations of the irreducible components and show that the desingularization construction is compatible with the natural projections between the parahoric subgroups.

通过某些线性代数条件，可以在格拉斯曼的乘积内实现 A 型志摩拉（Shimura）变体的局部模型。劳蒙（Laumon）提出了一种概括，它可以与线上的一个族相鉴别，这个族的一般纤维是循环簇的簇格拉斯曼，特殊纤维是循环簇的某个簇格拉斯曼。整个族位于仿射格拉斯曼的盖茨高里中心退化内。我们利用簇表示的机制研究了 A 型任意准子群的（复）劳蒙局部模型特殊纤维的性质。我们描述了有关簇格拉斯曼的群作用的不可还原成分和自然层。我们还构建了单元分解，并对相应的单元集合进行了明确描述。最后，我们研究了不可还原成分的去晶化性质，并证明了去晶化构造与准子群之间的自然投影是兼容的。

引用次数: 0

Period integrals of smooth projective complete intersections as exponential periods 作为指数周期的光滑投影完全相交的周期积分

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-11-05 DOI: 10.1016/j.jpaa.2024.107836

Jeehoon Park

Let X be a smooth projective complete intersection over

Q

of dimension

n - k

in the projective space

P_{Q}^{n}

defined by the zero locus of

\underline{f} (\underline{x}) = (f_{1} (\underline{x}), \dots, f_{k} (\underline{x}))

, for given positive integers n and k. For a given primitive homology cycle

[γ] \in H_{n - k} {(X (C), Z)}_{0}

, the period integral is defined to be a linear map from the primitive de Rham cohomology group

H_{d R, prim}^{n - k} (X (C); Q)

C

given by

[ω] \mapsto \int_{γ} ω

. The goal of this article is to interpret this period integral as Feynman's path integral of 0-dimensional quantum field theory with the action functional

S = \sum_{ℓ = 1}^{k} y_{ℓ} f_{ℓ} (\underline{x})

(in other words, the exponential period with the action functional S) and use this interpretation to develop a formal deformation theory of period integrals of X, which can be viewed as a modern deformation theoretic treatment of the period integrals based on the Maurer-Cartan equation of a dgla (differential graded Lie algebra).

设 X 是在给定正整数 n 和 k 的投影空间 PQn 中，维数为 n-k 的 Q 上的光滑投影完全交，其定义为 f_(x_)=(f1(x_),⋯,fk(x_)) 的零点。对于给定的原始同调周期 [γ]∈Hn-k(X(C),Z)0，周期积分被定义为从原始 de Rham 同调群 HdR,primn-k(X(C);Q) 到 C 的线性映射，由 [ω]↦∫γω 给定。本文的目的是把这个周期积分解释为0维量子场论的费曼路径积分，其作用函数为S=∑ℓ=1kyℓfℓ(x_)（换句话说、的指数周期），并利用这一解释发展了 X 周期积分的形式变形理论，这可以看作是基于微分级列代数的毛勒-卡尔坦方程对周期积分的现代变形理论处理。

引用次数: 0

GT-shadows for the gentle version GTˆgen of the Grothendieck-Teichmueller group 格罗登第克-泰赫穆勒群温柔版 GTˆgen 的 GT 阴影

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-31 DOI: 10.1016/j.jpaa.2024.107819

Vasily A. Dolgushev , Jacob J. Guynee

Let

B_{3}

be the Artin braid group on 3 strands and

{PB}_{3}

be the corresponding pure braid group. In this paper, we construct the groupoid

GTSh

GT

-shadows for a (possibly more tractable) version

{\hat{GT}}_{0}

of the Grothendieck-Teichmueller group

\hat{GT}

introduced in paper [12] by D. Harbater and L. Schneps. We call this group the gentle version of

\hat{GT}

and denote it by

{\hat{GT}}_{g e n}

. The objects of

GTSh

are finite index normal subgroups

N

B_{3}

satisfying the condition

N \leq {PB}_{3}

. Morphisms of

GTSh

are called

GT

-shadows and they may be thought of as approximations to elements of

{\hat{GT}}_{g e n}

. We show how

GT

-shadows can be obtained from elements of

{\hat{GT}}_{g e n}

and prove that

{\hat{GT}}_{g e n}

is isomorphic to the limit of a certain functor defined in terms of the groupoid

GTSh

. Using this result, we get a criterion for identifying genuine

GT

-shadows.

假设 B3 是 3 股上的阿廷辫状群，PB3 是相应的纯辫状群。在本文中，我们为 D. Harbater 和 L. Schneps 在论文[12]中介绍的格罗内迪克-泰希姆勒群 GTˆ 的一个（可能更容易理解的）版本 GTˆ0 构建了 GT 阴影的类群 GTSh。我们称这个群为 GTˆ 的温柔版本，用 GTˆgen 表示。GTSh 的对象是满足 N≤PB3 条件的 B3 的有限索引正则子群 N。GTSh 的变形被称为 GT-阴影，它们可以被看作是 GTˆgen 元素的近似。我们展示了如何从 GTˆgen 的元素中得到 GT 影，并证明 GTˆgen 与以群集 GTSh 定义的某个函子的极限同构。

引用次数: 0

On the Gowers trick for classical simple groups 关于经典简单群的高尔斯诀窍

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-28 DOI: 10.1016/j.jpaa.2024.107833

Francesco Fumagalli , Attila Maróti

If A, B, C are subsets in a finite simple group of Lie type G at least two of which are normal with

| A | | B | | C |

relatively large, then we establish a stronger conclusion than

A B C = G

. This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.

如果 A、B、C 是有限简单李型群 G 中的子集，其中至少有两个子集是正常的，且 |A||B||C|| 相对较大，那么我们就建立了比 ABC=G 更强的结论。

引用次数: 0

Flat relative Mittag-Leffler modules and Zariski locality 扁平相对米塔格-列夫勒模块和扎里斯基位置

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-28 DOI: 10.1016/j.jpaa.2024.107834

Asmae Ben Yassine, Jan Trlifaj

The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in [26]. More recently, relative Mittag-Leffler modules were employed in the theory of (infinitely generated) tilting modules and the associated quasi-coherent sheaves, [2], [22]. Here, we study the ascent and descent along flat and faithfully flat homomorphisms for relative versions of the Mittag-Leffler property. In particular, we prove the Zariski locality of the notion of a locally f-projective quasi-coherent sheaf for all schemes, and for each

n \geq 1

, of the notion of an n-Drinfeld vector bundle for all locally noetherian schemes.

雷诺和格鲁森在[26]中证明（无限维）向量束概念的扎里斯基位置性时，米塔格-勒弗勒性质的上升和下降起了重要作用。最近，[2]、[22] 在（无限生成的）倾斜模块和相关准相干剪切理论中使用了相对米塔格-勒弗勒模块。在这里，我们研究了米塔格-勒弗勒性质相对版本的沿平坦和忠实平坦同态的上升和下降。特别是，我们证明了所有方案的局部 f投影准相干剪切概念的扎里斯基局域性，以及所有局部无醚方案的 n-Drinfeld 向量束概念的每个 n≥1 的扎里斯基局域性。

引用次数: 0

Almost Gorenstein simplicial semigroup rings 几乎戈伦斯坦简单半群环

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-26 DOI: 10.1016/j.jpaa.2024.107835

Kazufumi Eto , Naoyuki Matsuoka , Takahiro Numata , Kei-ichi Watanabe

We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determine 2-dimensional normal semigroup rings which have “Ulrich elements” defined in [8].

我们给出了与简单半群相关的半群环的几乎戈伦斯坦性质的标准。我们将纳里关于几乎对称数字半群的定理推广到阶数更高的简单半群。根据这一标准，我们确定了具有 [8] 中定义的 "乌尔里希元素 "的二维正常半群环。

引用次数: 0

DK conjecture for some K-inequivalences from Grassmannians 一些格拉斯曼 K-inequivalences 的 DK 猜想

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-24 DOI: 10.1016/j.jpaa.2024.107831

Naichung Conan Leung , Ying Xie

The DK conjecture of Bondal-Orlov [1] and Kawamata [2] states that there should be an embedding of bounded derived categories for any K-inequivalence, which is proved to be true for the toroidal case ([3], [4], [5] and [6]). In this paper, we construct examples of non-toroidal K-inequivalences from Grassmannians inspired by [7], [8], [9] and [10], and we show that these K-inequivalences satisfy the DK conjecture.

邦达尔-奥洛夫[1]和川俣[2]的 DK 猜想指出，任何 K-inequivalence 都应该有一个有界派生范畴的嵌入，这在环面情况下被证明是正确的（[3]、[4]、[5] 和 [6]）。本文受[7]、[8]、[9]和[10]的启发，从格拉斯曼中构造了非环状 K-inequivalences 的例子，并证明这些 K-inequivalences 满足 DK 猜想。

引用次数: 0

The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables 二变量多项式 R 代数的局部零势 R 派生的中心子

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107828

M'hammed El Kahoui, Najoua Essamaoui, Mustapha Ouali

Let R be an integral domain containing

Q

and ξ be an irreducible nontrivial locally nilpotent R-derivation of the polynomial R-algebra A in two variables. In this paper we investigate the group

{Aut}_{R} (A, ξ)

of R-automorphisms of A which commute with ξ. In the case R is a unique factorization domain and the plinth ideal of ξ is principal we give a complete description of the subgroup

{SAut}_{R} (A, ξ)

{Aut}_{R} (A, ξ)

consisting of Jacobian one automorphisms. If moreover R contains a field K such that the group of units of R is

K^{⋆}

we prove that

{Aut}_{R} (A, ξ) = {SAut}_{R} (A, ξ)

设 R 是包含 Q 的积分域，ξ 是两变量多项式 R 代数 A 的不可还原的非琐局部无穷 R 衍射。在本文中，我们将研究与ξ换元的 A 的 R 自变量群 AutR(A,ξ)。在 R 是唯一因式分解域且 ξ 的柱顶理想是主理想的情况下，我们给出了 AutR(A,ξ) 的子群 SAutR(A,ξ) 的完整描述，该子群由雅各布一自形化组成。如果 R 还包含一个域 K，使得 R 的单位群是 K⋆，我们就可以证明 AutR(A,ξ)=SAutR(A,ξ)。

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引用次数: 0

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