Journal of Pure and Applied Algebra最新文献

英文中文

Translational hulls of semigroups of endomorphisms of an algebra 代数的自同态半群的平移壳

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-04-01 Epub Date: 2026-02-24 DOI: 10.1016/j.jpaa.2026.108203

Victoria Gould , Ambroise Grau , Marianne Johnson , Mark Kambites

We consider the translational hull

Ω (I)

of an arbitrary subsemigroup I of an endomorphism monoid

End (A)

where A is a universal algebra. We give conditions for every bi-translation of I to be realised by transformations, or by endomorphisms, of A. We demonstrate that certain of these conditions are also sufficient to provide natural isomorphisms between the translational hull of I and the idealiser of I within

End (A)

, which in the case where I is an ideal is simply

End (A)

. We describe the connection between these conditions and work of Petrich and Gluskin in the context of densely embedded ideals. Where the conditions fail, we develop a methodology to extract information concerning

Ω (I)

from the translational hull

Ω (I / \approx)

of a quotient

I / \approx

of I. We illustrate these concepts in detail in the cases where A is: a free algebra; an independence algebra; a finite symmetric group.

考虑自同态单群端(A)的任意子半群I的平移壳Ω(I)，其中A是一个泛代数。我们给出了通过A的变换或自同态来实现I的每一个双平移的条件。我们证明了这些条件中的某些条件也足以提供I的平移外壳与末端(A)中I的理想化器之间的自然同构，在这种情况下，I是一个理想只是末端(A)。我们描述了这些条件与Petrich和Gluskin在密集嵌入理想的背景下的工作之间的联系。当条件不满足时，我们开发了一种方法，从I的商I/≈的平移壳Ω（I/≈）中提取有关Ω(I)的信息。我们在以下情况下详细说明了这些概念：a是一个自由代数；独立代数；有限对称群。

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引用次数: 0

Measuring comodules and enrichment 测量模块和富集

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-24 DOI: 10.1016/j.jpaa.2026.108211

Martin Hyland , Ignacio López Franco , Christina Vasilakopoulou

This paper extends the theory of universal measuring comonoids to modules and comodules in braided monoidal categories. We generalise the universal measuring comodule

Q (M, N)

, originally introduced for modules over

k

-algebras when

k

is a field, to arbitrary braided monoidal categories. In order to establish its existence, we prove a representability theorem for presheaves on opfibred categories and an adjoint functor theorem for opfibred functors. The global categories of modules and comodules, fibred and opfibred over monoids and comonoids respectively, are shown to exhibit an enrichment of modules in comodules. Additionally, we use our framework to study higher derivations of algebras and modules, defining along the way the non-commutative Hasse-Schmidt algebra.

本文将广义度量共子体理论推广到编织一元范畴中的模和模。我们将广义测量模Q（M，N）推广到任意编织一元范畴，该广义测量模Q（M，N）最初是在k-代数上当k是一个域时引入的。为了证明它的存在性，我们证明了上光范畴上的预层的可表示性定理和上光函子的伴随函子定理。模和模的整体范畴，单模和共模上分别是纤维的和非纤维的，在模中显示出模的丰富。此外，我们使用我们的框架来研究代数和模块的高阶导数，并在此过程中定义非交换的Hasse-Schmidt代数。

引用次数: 0

Morita invariants of quasitriangular coideal subalgebras 拟三角共理想子代数的Morita不变量

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108210

Monique Müller , Chelsea Walton

We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular coideal subalgebras. Such categories form a prevalent class of braided module categories. This is analogous to how representations of braid groups of Coxeter type A produce invariants of representation categories of quasitriangular Hopf algebras, a prevalent class of braided monoidal categories. This work also includes concrete examples, and classification results for K-matrices of quasitriangular coideal subalgebras.

利用Coxeter型BC和D型辫群的表示，给出了拟三角共理想子代数表示范畴的不变量。这样的类别形成了一个流行的编织模块类别。这类似于Coxeter型A的编织群的表示如何产生拟三角形Hopf代数（一种流行的编织一元范畴）的表示范畴的不变量。本文还包括拟三角共理想子代数k矩阵的具体实例和分类结果。

引用次数: 0

On Rota-Baxter vertex operator algebras 关于Rota-Baxter顶点算子代数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108202

Chengming Bai , Li Guo , Jianqi Liu , Xiaoyan Wang

Rota-Baxter operators, which can be viewed as the integral counterpart of derivations on algebras and operator forms of the classical Yang-Baxter equation, are defined and studied for vertex (operator) algebras. Examples of such operators are constructed for various vertex operator algebras. The closely related notion of dendriform algebras is also defined for vertex operator algebras. It is shown that the Rota-Baxter operators and dendriform structures give rise to new examples of vertex (Leibniz) algebras and vertex algebras without vacuum. The classical relations among dendriform algebras, associative algebras, Rota-Baxter algebras, and pre-Lie algebras are also extended to their vertex algebra analogs.

定义并研究了顶点（算子）代数的Rota-Baxter算子，它可以看作是代数上的导数和经典Yang-Baxter方程算子形式的积分对应物。这种算子的例子是为各种顶点算子代数构造的。密切相关的树形代数的概念也被定义为顶点算子代数。证明了Rota-Baxter算子和树形结构产生了顶点（莱布尼兹）代数和无真空顶点代数的新例子。树形代数、结合代数、Rota-Baxter代数和pre-Lie代数之间的经典关系也被推广到它们的顶点代数类似物。

引用次数: 0

Two invariant subalgebras of rational Cherednik algebras 有理Cherednik代数的两个不变子代数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jpaa.2026.108190

Gwyn Bellamy, Misha Feigin, Niall Hird

Originally motivated by connections to integrable systems, two natural subalgebras of the rational Cherednik algebra have been considered in the literature. The first is the subalgebra of all degree zero elements and the second is the Dunkl angular momentum subalgebra.

In this article, we study the ring-theoretic and homological properties of these algebras. Our approach is to realise them as rings of invariants under the action of certain reductive subgroups of

{SL}_{2}

. This allows us to describe their centres. Moreover, we show that they are Auslander–Gorenstein and Cohen–Macaulay and, at

t = 0

, give rise to prime PI-algebras whose PI-degree we compute.

Since the degree zero subalgebra can be realized as the ring of invariants for the maximal torus

T \subset {SL}_{2}

and the action of this torus on the rational Cherednik algebra is Hamiltonian, we also consider its (quantum) Hamiltonian reduction with respect to T. At

t = 1

, the quantum Hamiltonian reduction of the spherical subalgebra is a filtered quantization of the quotient of the minimal nilpotent orbit closure

{\overline{O}}_{\min}

gl (n)

by the reflection group W. At

t = 0

, we get a graded Poisson deformation of the symplectic singularity

{\overline{O}}_{\min} / W

最初的动机是连接到可积系统，在文献中考虑了有理Cherednik代数的两个自然子代数。第一个是所有零次元的子代数，第二个是Dunkl角动量子代数。在本文中，我们研究了这些代数的环论性质和同调性质。我们的方法是在SL2的某些约化子群的作用下将它们实现为不变量环。这使我们能够描述它们的中心。此外，我们证明了它们是Auslander-Gorenstein和Cohen-Macaulay，并且在t=0时，产生了质数pi -代数，我们计算了它们的pi度。由于0次子代数可以实现为最大环面T∧SL2的不变量环，并且这个环面对有理性Cherednik代数的作用是哈密顿的，我们也考虑它关于T的（量子）哈密顿约简，在T =1时，球面子代数的量子哈密顿约简是最小幂零轨道闭包O在gl(n)中的商被反射群w在T =0时的过滤量子化，我们得到了O - min/W型辛奇点的一个梯度泊松变形。

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引用次数: 0

Skew Symmetric Extended Affine Lie algebras 斜对称扩展仿射李代数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jpaa.2026.108188

S. Eswara Rao , Priyanshu Chakraborty

For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we study irreducible integrable modules for SSEALA with finite dimensional weight spaces. We classify all such modules in the level zero case with non degenerate skew symmetric matrix.

对于任何复数上的斜对称矩阵，我们引入了一个斜对称扩展仿射李代数（SSEALA）。这样我们就得到了一个大的eala类，大多数情况下它们是非同构的。本文研究具有有限维权空间的SSEALA的不可约可积模。我们用非退化的斜对称矩阵对所有这些零阶模进行了分类。

引用次数: 0

Infinitesimal R-matrices for some families of Hopf algebras 一些Hopf代数族的无穷小r矩阵

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108205

Lucrezia Bottegoni , Fabio Renda , Andrea Sciandra

Given a bialgebra H such that the associated trivial topological bialgebra

H [[ħ]]

admits a quasitriangular structure

\tilde{R} = R (1 \otimes 1 + ħ χ + O (ħ^{2}))

, one gets a distinguished element

χ \in H \otimes H

which is an infinitesimal

R

-matrix, according to the definition given in [1]. In this paper we classify infinitesimal

R

-matrices for some families of well-known Hopf algebras, among which are the generalized Kac–Paljutkin Hopf algebras

H_{2 n^{2}}

, the Radford Hopf algebras

H_{(r, n, q)}

, and the Hopf algebras

E (n)

给定一个双代数H，使得所关联的平凡拓扑双代数H[[H]]具有准三角形结构R≈=R（1⊗1+ħχ+O（ħ2）），根据[1]给出的定义，可以得到一个显著元素χ∈H⊗H，它是一个无穷小的R矩阵。本文对一些已知Hopf代数族的无穷小r矩阵进行了分类，其中包括广义Kac-Paljutkin Hopf代数H2n2、Radford Hopf代数H（r,n,q）和Hopf代数E(n)。

引用次数: 0

Graph complexes and deformation theories of the (wheeled) properads of quasi- and pseudo-Lie bialgebras 拟和伪李双代数（轮）性质的图复形和变形理论

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-24 DOI: 10.1016/j.jpaa.2026.108204

Oskar Frost

Quasi-Lie bialgebras are natural extensions of Lie bialgebras, where the cobracket satisfies the co-Jacobi relation up to some natural obstruction controlled by a skew-symmetric 3-tensor ϕ. This structure was introduced by Drinfeld while studying deformation theory of universal enveloping algebras and has since seen many other applications in algebra and geometry. In this paper we study the derivation complex of strongly homotopy quasi-Lie bialgebra, both in the unwheeled (i.e. standard) and wheeled case, and compute its cohomology in terms of Kontsevich graph complexes.

拟李双代数是李双代数的自然扩展，其中协括号满足co-Jacobi关系，直至由偏对称3张量φ控制的自然障碍物。这种结构是由Drinfeld在研究通用包络代数的变形理论时引入的，此后在代数和几何中得到了许多其他应用。本文研究了非轮式（即标准）和轮式两种情况下强同伦拟李双代数的导数复形，并用Kontsevich图复形计算了其上同调。

引用次数: 0

Infinite dimensional modules for linear algebraic groups 线性代数群的无限维模

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-24 DOI: 10.1016/j.jpaa.2026.108206

Eric M. Friedlander

We investigate infinite dimensional modules for a linear algebraic group

G

over a field of positive characteristic p. For any subcoalgebra

C \subset O (G)

of the coordinate algebra of

G

, we consider the abelian subcategory

C o M o d (C) \subset M o d (G)

and the left exact functor

{(-)}_{C} : M o d (G) \to C o M o d (C)

that is right adjoint to the inclusion functor. The class of cofinite

G

-modules is formulated using finite dimensional subcoalgebras of

O (G)

and the polynomial growth of various examples of cofinite modules is computed.

Infinite dimensional

G

-modules of particular interest are those which are mock injective. Various examples of mock injective modules are investigated. For almost all linear algebraic groups

G

, every mock injective

G

-module J satisfies the condition that

H o m_{G} (J, M) = 0

whenever

M = M_{C}

for some finite dimensional sub-coalgebra

C \subset O (G)

我们研究线性代数群G在一个正特征域p上的无穷维模。对于G的坐标代数的任意子代数C∧O(G)，我们考虑与包含函子右伴随的阿贝子范畴CoMod(C)∧Mod(G)和左精确函子（−）C:Mod(G)→CoMod(C)。利用O(G)的有限维子代数构造了有限G模的类，并计算了各种有限模的多项式增长。特别有趣的无限维g模是那些模拟内射的模。研究了模拟注入模块的各种示例。对于几乎所有线性代数群G，对于某有限维子代数C∧O(G)，每个拟内射G模J满足当M=MC时HomG(J，M)=0的条件。

引用次数: 0

On the strong Sarkisov program 关于强大的萨尔基索夫计划

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108208

Yang He

In this paper, we showed that the strong Sarkisov program in dimension d can be derived from the termination of specific log flips in dimension

\leq d - 1

. As a corollary, we prove that the strong Sarkisov program holds in dimension 4. Additionally, we prove the weak Sarkisov program with decreasing (augmented) Sarkisov degree. Finally, using the theory of syzygies of Mori fibre spaces, we obtain a directed diagram that encodes the information of the strong Sarkisov program.

在本文中，我们证明了d维的强Sarkisov规划可以由维数≤d−1的特定对数翻转的终止导出。作为推论，我们证明了强Sarkisov规划在四维空间中成立。此外，我们还证明了具有递减（增广）Sarkisov度的弱Sarkisov方案。最后，利用Mori纤维空间的协同理论，得到了一个编码强Sarkisov规划信息的有向图。

引用次数: 0

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