Journal of Pure and Applied Algebra最新文献

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GAGA type results for singularity categories 奇异类的GAGA型结果

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108146

Yilin Wu , Jinyi Xu , Guodong Zhou

Several GAGA-type results for singularity categories are presented. Firstly, as an easy consequence of Serre's GAGA theorem, we show that for a complex projective variety, its singularity category is naturally equivalent to that of its analytification.

Secondly, we introduce the torsion singularity category of a formal scheme. Under Orlov's (ELF) condition, we prove that for the formal completion of a Noetherian scheme along a closed subset, its torsion singularity category is equivalent to the singularity category of the original scheme, with support in the closed subset.

Lastly, using the Artin Approximation Theorem and the result above, we provide an alternative proof of a result of Orlov. Namely, for a Noetherian local ring with an isolated singularity, its singularity category is equivalent (up to direct summands) to that of its Henselization, which in turn is equivalent to that of its completion.

给出了奇异类的几个ga型结果。首先，作为Serre’s GAGA定理的一个简单推论，我们证明了对于一个复杂的射影变，它的奇异范畴自然等价于它的分析范畴。其次，我们引入了一种形式格式的扭转奇点范畴。在Orlov （ELF）条件下，证明了Noetherian方案沿闭子集的形式完备时，其扭转奇异范畴等价于原方案的奇异范畴，并在闭子集上有支撑。最后，利用Artin近似定理和上述结果，我们提供了Orlov结果的另一种证明。也就是说，对于一个具有孤立奇点的noether局部环，其奇点范畴（直到直求和）等价于它的Henselization的范畴，而Henselization又等价于它的补全。

引用次数: 0

Horrocks' theorem for odd orthogonal groups 奇正交群的Horrocks定理

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108142

A.A. Ambily, H. Sugilesh

We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring

R [X]

, over a commutative ring R in which 2 is invertible, as a product of an orthogonal matrix with entries in R and an elementary orthogonal matrix with entries from

R [X]

本文证明了奇初等正交群的Horrocks定理，该定理给出了在交换环R（2可逆）上，含有多项式环R[X]元素的正交矩阵分解为含有R元素的正交矩阵与含有R[X]元素的初等正交矩阵的乘积。

引用次数: 0

Which categories are varieties of quantitative algebras? 哪些类别是数量代数的变种？

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108139

Jiří Adámek

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms).

经典的变种被Lawvere描述为具有有效同余的范畴和一个变种生成器：一个抽象有限的正则生成器，它是正则投影的（它的同函子保留正则的外胚）。我们将Mardare， Panangaden和Plotkin的数量代数的变种类似地描述为度量丰富的范畴。我们引入了次同余的概念（同余的一个度量丰富的类似物）和相应的次正则上胚，通过次同余的极限得到。定量代数的变种正是具有有效次同余的富度量范畴和一个次变量生成：一个抽象有限的次正则生成，它是次正则投影（它的同函子保留了次正则上胚）。

引用次数: 0

Raney extensions: A pointfree theory of T0 spaces based on canonical extension Raney扩展：基于规范扩展的T0空间无点理论

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108137

Anna Laura Suarez

<div><div>We introduce a pointfree version of Raney duality. Our objects are Raney extensions of frames, pairs <math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math> where C is a coframe and <math><mi>L</mi><mo>⊆</mo><mi>C</mi></math> is a subframe that meet-generates it and whose embedding preserves strongly exact meets. We show that there is a dual adjunction between Raney and Top, with all <math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math> spaces as fixpoints, assigning to a space X the pair <math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math>, with <math><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> are the intersections of open sets. We show that for every Raney extension <math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math> there are subcolocale inclusions <math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mi>L</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>p</mi></mrow></msup><mo>⊆</mo><mi>C</mi><mo>⊆</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math> where <math><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math> is the coframe of fitted sublocales and <math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math> is the frame of joins of closed sublocales. We thus exhibit a symmetry between these two well-studied structures in pointfree topology. The spectra of these are, respectively, the classical spectrum <math><mrow><mi>pt</mi></mrow><mo>(</mo><mi>L</mi><mo>)</mo></math> of the underlying frame and its <math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math> spectrum <math><msub><mrow><mi>pt</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math>. This confirms the view advanced in [9] that sobriety and the <math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math> property are mirror images of each other, and suggests that the symmetry above is a pointfree view of it. All Raney extensions satisfy some variation of the properties density and compactness from the theory of canonical extensions. We characterize sobriety, the <math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, and the <math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math> axioms in terms of density and compactness of <math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math>. We characterize frame morphisms <math><mi>f</mi><mo>

我们引入了Raney二象性的无点版本。我们的对象是框架、对（L，C）的Raney扩展，其中C是一个余框，L C是一个满足生成余框的子框架，其嵌入保持强精确满足。我们证明了Raney和Top之间存在一个对偶共轭，以所有的T0空间为不动点，赋予空间X一对(Ω（X)，U(X)），其中U(X)是开集的交点。我们证明了对于每一个Raney扩展（L，C），都存在子域包体Sc(L)，其中So(L)为拟合子域的框架，Sc(L)为封闭子域的连接框架。因此，我们在无点拓扑中展示了这两个研究得很好的结构之间的对称性。它们的光谱分别是底层框架的经典谱pt(L)和它的TD谱ptD(L)。这证实了[9]中提出的观点，即清醒性和TD属性是彼此的镜像，并表明上面的对称性是它的无点视图。所有的Raney扩展都满足正则扩展理论中密度和紧性的一些变化。我们用密度和紧致性(Ω（X)，U(X)）来描述清醒、T1和TD公理。我们描述框架态射f:L→M，它扩展到框架态射f: （L，C）→（M，D）。因此，我们得到了框架f:L→M的态射的一个特征，它扩展到框架f: Sc(L)→Sc(M)的态射，回答了[7]中提出的一个问题。我们证明了坐标系上自由Raney扩展的存在性。我们证明了所有的Raney扩展都承认一个清醒的共同反思。将Raney的态射限制为精确态射，可以同时得到无协对象和TD反射。最后，我们证明了局部紧坐标系（[21]中引入）的正则扩展是自由代数Raney扩展。我们还给出了TD对偶性的一个新观点：与框架情况相比，TD空间是Raney的满子范畴，不需要限制态射。

引用次数: 0

Weight conjectures for Parker–Semeraro fusion systems Parker-Semeraro聚变系统的重量猜想

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108140

Radha Kessar , Jason Semeraro , Patrick Serwene , İpek Tuvay

We prove that the Parker–Semeraro systems satisfy six of the nine Kessar–Linckelmann–Lynd–Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of

Aut (G_{2} (3))

, the principal 5-blocks of HN, BM,

Aut (H N)

, Ly, the principal 7-block of M, and the principal p-blocks of

G_{2} (p)

for

p \geq 3

我们证明了Parker-Semeraro系统满足饱和聚变系统的9个kessar - linckelmann - lind - semeraro权猜想中的6个。作为一个副产品，我们得到了Robinson的常权猜想对于Aut（G2(3)）的主3块，HN的主5块，BM, Aut(HN), Ly， M的主7块，以及对于p≥3的G2(p)的主p块成立。

引用次数: 0

On braided Hopf structures on exterior algebras 外代数上的编织Hopf结构

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-12-01 DOI: 10.1016/j.jpaa.2025.108135

Rinat Kashaev , Vladimir Mangazeev

We show that the exterior algebra of a vector space V of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis.

A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang–Baxter equation. These solutions are conjectured to give rise to the two-variable Links–Gould polynomial invariants associated with the super-quantum group

U_{q} (gl (N | 1))

, where

N = \dim (V)

. We support this conjecture through computations for small values of N.

我们证明了维数大于1的向量空间V的外部代数允许一个单参数编织Hopf代数结构族，这是由它与Nichols代数的认同引起的。我们在自然集合论的基础上显式地计算结构常数。存在一个单参数对角自同构族，我们用它来构造（常）Yang-Baxter方程的解。这些解被推测为产生与超量子群Uq（gl(N|1)）相关的双变量Links-Gould多项式不变量，其中N=dim (V)。我们通过计算小的N值来支持这个猜想。

引用次数: 0

An extension of the group of flows method for finite pre-Lie rings 有限预李环流动群方法的推广

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-11-10 DOI: 10.1016/j.jpaa.2025.108128

Agata Smoktunowicz

This paper presents an extension of the classical method [1] for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality

p^{n}

with p prime and n larger than p can be obtained with our extension.

本文给出了群与预李环相关联的经典方法[1]的推广。这种增强有望帮助我们更好地理解用于研究Yang-Baxter方程和Hopf-Galois扩展的集合论解的对象，称为括号。我们还证明了可以用我们的推广得到若干类p '和n大于p的基数pn的大括号。

引用次数: 0

A Tate algebra version of the Jacobian conjecture 雅可比猜想的泰特代数版本

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-11-10 DOI: 10.1016/j.jpaa.2025.108129

Lucas Hamada, Kazuki Kato, Ryo Komiya

This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as the Tate-Jacobian conjecture, for commutative rings R equipped with an I-adic topology. We show that if the I-adic topology on R is Hausdorff and

R / I

is a subring of a

Q

-algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if

R / I

has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for

C

is equivalent to the following statement: for all but finitely many primes p, the inverse of a polynomial map over

C_{p}

whose Jacobian determinant is an element of

C_{p}^{\times}

lies in the Tate algebra over

C_{p}

本文研究了具有i进进拓扑的交换环R的雅可比猜想的一个Tate代数版本，称为Tate-Jacobian猜想。我们证明了如果R上的I进拓扑是Hausdorff，并且R/I是q代数的子代数，那么特-雅可比猜想等价于雅可比猜想。相反，如果R/I具有正特征，则Tate-Jacobian猜想失效。进一步，我们证明了C的雅可比猜想等价于以下陈述：对于除有限多个素数p外的所有素数p，其雅可比行列式是cpx的一个元素的Cp上的多项式映射的逆存在于Cp上的Tate代数中。

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引用次数: 0

On tensor products of representations of Lie superalgebras 李超代数表示的张量积

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-11-10 DOI: 10.1016/j.jpaa.2025.108130

Abhishek Das , Santosha Pattanayak

We consider typical finite dimensional complex irreducible representations of a basic classical Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for

sl (m + 1, n + 1)

osp (2, 2 n)

G (3)

and

F (4)

under some assumptions. This result is a Lie superalgebra analogue of Rajan's fundamental result [10] on unique factorization of tensor products for finite dimensional complex simple Lie algebras.

考虑一类基本经典李超代数的典型有限维复不可约表示，给出了这种表示的有限张量积的唯一分解成立的充分条件。在某些假设条件下，证明了单非典型有限维不可约模sl(m+1,n+1), osp(2,2n)， G(3)和F(4)的张量积的唯一分解。这个结果是Rajan关于有限维复单李代数张量积唯一分解的基本结果[10]的李超代数模拟。

引用次数: 0

Starfish lemma via birational quasi-isomorphisms 通过两族拟同构的海星引理

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-11-07 DOI: 10.1016/j.jpaa.2025.108127

Dmitriy Voloshyn

We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.

研究了具有几何型簇结构的正规noether域之间的两族拟同构。我们证明了一个类似的海星引理，允许一个转移各种簇和代数性质的一个品种到另一个。特别地，我们开发了证明上簇代数等于给定交换环的工具。

引用次数: 0

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