Journal of Algebra and Its Applications最新文献

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Weak Hopf algebras, smash products and applications to adjoint-stable algebras 弱霍普夫布拉斯、粉碎乘积及其在邻接稳定布拉斯中的应用

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2024-01-24 DOI: 10.1142/s0219498825501567

Zhimin Liu, Shenglin Zhu

For a semisimple quasi-triangular Hopf algebra $(H, R)$ over a field $k$ of characteristic zero, and a strongly separable quantum commutative $H$ -module algebra $A$ , we show that $A # H$ is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra $End A^{*} \otimes H$ . With these structures, $_{A # H} Mod$ is the monoidal category introduced by Cohen and Westreich, and $_{End A^{*} \otimes H} ℳ$ is tensor equivalent to $_{H} ℳ$ . If $A$ is in the Müger center of $_{H} ℳ$ , then the embedding is a quasi-triangular weak Hopf algebra morphism. This explains the presence of a subgroup inclusion in the characterization of irreducible Yetter–Drinfeld modules for a finite group algebra.

对于特征为零的域 k 上的半简单准三角形霍普夫代数（H,R）和强可分离量子交换 H 模块代数 A，我们证明 A#H 是弱霍普夫代数，并且它可以嵌入弱霍普夫代数 EndA∗⊗H 中。有了这些结构，A#HMod 就是科恩和韦斯特里希引入的单元范畴，而 EndA∗⊗Hℳ 与 Hℳ 是张量等价的。如果 A 位于 Hℳ 的 Müger 中心，那么嵌入就是准三角形弱霍普夫代数态射。这就解释了在有限群代数的不可还原Yetter-Drinfeld模块的表征中存在子群包含的原因。

引用次数: 0

Cohomology of modified Rota–Baxter Leibniz algebra of weight λ 权重 λ 的修正罗塔-巴克斯特莱布尼兹代数的同调

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2024-01-24 DOI: 10.1142/s0219498825501579

Bibhash Mondal, Ripan Saha

Rota–Baxter operators have been paid much attention in the last few decades as they have many applications in mathematics and physics. In this paper, our object of study is modified Rota–Baxter operators on Leibniz algebras. We investigate modified Rota–Baxter Leibniz algebras from the cohomological point of view. We study a one-parameter formal deformation theory of modified Rota–Baxter Leibniz algebras and define the associated deformation cohomology that controls the deformation. Finally, as an application, we characterize equivalence classes of abelian extensions in terms of second cohomology groups.

由于 Rota-Baxter 算子在数学和物理学中的广泛应用，它在过去几十年里受到了广泛关注。本文的研究对象是莱布尼兹代数上的修正罗塔-巴克斯特算子。我们从同调的角度研究修正的 Rota-Baxter 莱布尼兹代数。我们研究了修正 Rota-Baxter 莱布尼兹代数的单参数形式变形理论，并定义了控制变形的相关变形同调。最后，作为一个应用，我们用第二同调群来描述无性扩展的等价类。

引用次数: 0

Kostant’s generating functions and Mckay–Slodowy correspondence 科斯坦特生成函数和姆凯-斯洛多耶对应关系

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2024-01-19 DOI: 10.1142/s0219498825501713

Naihuan Jing, Zhijun Li, Danxia Wang

Let $N ⊴ G$ be a pair of finite subgroups of ${SL}_{2} (ℂ)$ and $V$ a finite-dimensional fundamental $G$ -module. We study Kostant’s generating functions for the decomposition of the ${SL}_{2} (ℂ)$ -module $S^{k} (V)$ restricted to $N ◃ G$ in connection with the McKay–Slodowy correspondence. In particular, the classical Kostant formula was generalized to a uniform version of the Poincaré series for the symmetric invariants in which the multiplicities of any individual module in the symmetric algebra are completely determined.

设 N⊴G 是 SL2(ℂ) 的一对有限子群，V 是有限维基 G 模块。我们结合麦凯-斯洛多维对应关系，研究限制于 N◃G 的 SL2(ℂ)-Module Sk(V) 分解的科斯坦生成函数。特别是，经典的科斯坦公式被推广为对称不变式的统一版本的波恩卡列数列，其中对称代数中任何单个模块的乘数都是完全确定的。

引用次数: 0

Duplex Hecke algebras of type B B 型双联赫克代数

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2024-01-10 DOI: 10.1142/s021949882550166x

Yu Xie, An Zhang, Bin Shu

As a sequel to [C. Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in Algebra Colloq.], in this article we first introduce a so-called duplex Hecke algebras of type <math altimg="eq-00003.gif" display="inline" overflow="scroll"><mstyle mathvariant="sans-serif"><mi>B</mi></mstyle></math> which is a <math altimg="eq-00004.gif" display="inline" overflow="scroll"><mi>ℚ</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo></math>-algebra associated with the Weyl group <math altimg="eq-00005.gif" display="inline" overflow="scroll"><mi mathvariant="script">𝒲</mi><mo stretchy="false">(</mo><mstyle mathvariant="sans-serif"><mi>B</mi></mstyle><mo stretchy="false">)</mo></math> of type <math altimg="eq-00006.gif" display="inline" overflow="scroll"><mstyle mathvariant="sans-serif"><mi>B</mi></mstyle></math>, and symmetric groups <math altimg="eq-00007.gif" display="inline" overflow="scroll"><msub><mrow><mi>𝔖</mi></mrow><mrow><mi>l</mi></mrow></msub></math> for <math altimg="eq-00008.gif" display="inline" overflow="scroll"><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>m</mi></math>, satisfying some Hecke relations (see Definition 3.1). This notion originates from the degenerate duplex Hecke algebra arising from the course of study of a kind of Schur–Weyl duality of Levi-type (see [B. Shu and Y. Yao, On enhanced reductive groups (I): Enhanced Schur algebras and the dualities related to degenerate duplex Hecke algebras, with an appendix by B. Liu, submitted (2023)]), extending the duplex Hecke algebra of type <math altimg="eq-00009.gif" display="inline" overflow="scroll"><mstyle mathvariant="sans-serif"><mi>A</mi></mstyle></math> arising from the related <math altimg="eq-00010.gif" display="inline" overflow="scroll"><mi>q</mi></math>-Schur–Weyl duality of Levi-type (see [C. Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in Algebra Colloq.]). A duplex Hecke algebra of type <math altimg="eq-00011.gif" display="inline" overflow="scroll"><mstyle mathvariant="sans-serif"><mi>B</mi></mstyle></math> admits natural representations on certain tensor spaces. We then establish a Levi-type <math altimg="eq-00012.gif" display="inline" overflow="scroll"><mi>q</mi></math>-Schur–Weyl duality of type <math altimg="eq-00013.gif" display="inline" overflow="scroll"><mstyle mathvariant="sans-serif"><mi>B</mi></mstyle></math>, which reveals the double centralizer property between such duplex Hecke algebras and <math altimg="eq-00014.g

作为 [C. Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021, arXiv:2108.07587[math.RT]] 的续篇，已被接受。Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in Algebra Colloq.在本文中，我们首先介绍一种所谓的 B 型双工 Hecke 代数，它是一个与 B 型韦尔群𝒲(B) 和对称群𝔖l（l=0,1,...,m）相关联的ℚ(q)代数，满足一些 Hecke 关系（见定义 3.1）。这一概念源于对一种 Levi 型舒尔-韦尔对偶性的研究过程中产生的退化双工 Hecke 代数（见 [B. Shu and Y. Yao, On enhanced Hecke algebra] [中文版]）。Shu and Y. Yao, On enhanced reductive groups (I)：见[B. Shu and Y. Yao, On enhanced reductive groups (I): Enhanced Schur algebras and the dualities related to degenerate duplex Hecke algebras, with an appendix by B. Liu, submitted (2023)]], 扩展了由相关的 Levi 型 q-Schur-Weyl 对偶性产生的 A 型 duplex Hecke 代数（见[C. Xue and A. Zhang, Doulex Hecke algebra of type A arising from the related q-Schur-Weyl duality of Levi-type]）。Xue and A. Zhang, Doubled Hecke algebras and related quantum Schur duality, preprint (2021), arXiv:2108.07587[math.RT], accepted for publication in Algebra Colloq.）B 型双工赫克代数在某些张量空间上有自然表示。Bao and W. Wang, A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs, Astérisque402 (2018)].

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引用次数: 0

Two results on character codegrees 关于字符编码度的两个结果

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2024-01-10 DOI: 10.1142/s0219498825501580

Yang Liu, Yong Yang

Let $G$ be a finite group and $Irr (G)$ be the set of irreducible characters of $G$ . The codegree of an irreducible character $χ$ of the group $G$ is defined as $cod (χ) = | G : ker (χ) | / χ (1)$ . In this paper, we study two topics related to the character codegrees. The first result is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized only by graph theoretical terms. The second result is about the $p$ -parts of the codegrees and character degrees.

设 G 是有限群，Irr(G) 是 G 的不可还原字符集。群 G 的不可还原字符 χ 的度数定义为 cod(χ)=|G:ker(χ)|/χ(1)。在本文中，我们研究了与字符编码度相关的两个课题。第一个结果与字符 codegrees 的素数图有关，我们证明了几类群的 codegree 素数图只能用图论术语来表征。第二个结果是关于密码度和字符度的 p 部分。

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引用次数: 0

A type C study of braverman-gaitsgory-ginzburg'sconstruction of sln representations 布拉夫曼-盖茨戈里-金兹伯格的sln表征构造的C型研究

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2023-12-14 DOI: 10.1142/s0219498825501610

Zhijie Dong, Haitao Ma

. In [FMX19], it is proved that the convolution algebra of top Borel-Moore homology on Steinberg variety of type B/C realizes U ( sl θn ), where sl θn is the ﬁxed point subalgebra of involution on sl n . So top Borel-Moore homology of the partial Springer’s ﬁbers gives the representations of U ( sl θn ). In this paper, we study these representations using the Schur-Weyl duality and Springer theory.

.在 [FMX19] 中，证明了 B/C 型 Steinberg 变上的顶 Borel-Moore 同调的卷积代数实现了 U ( sl θn ) ，其中 sl θn 是 sl n 上反卷的定点子代数。因此，部分斯普林格的顶玻尔-摩尔同调给出了 U ( sl θn ) 的表示。在本文中，我们将利用舒尔-韦尔对偶性和斯普林格理论来研究这些表示。

引用次数: 0

Non-linear Jordan Triple *-Derivation on Prime *-Algebras 质*-代数上的非线性约旦三*-衍生

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2023-12-14 DOI: 10.1142/s0219498825501646

Ali Taghavi

引用次数: 0

Variations of primeness of ideals in rings of continuous functions 连续函数环中理想的原始性变化

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2023-12-14 DOI: 10.1142/s0219498825501683

A. R. Aliabad, M. Ghoulipour, M. Paimann

引用次数: 0

Partial actions of sweedler hopf algebra on generalized quaternion algebra 广义四元代数上的 sweedler hopf 代数的部分作用

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2023-12-14 DOI: 10.1142/s0219498825501592

Yong Deng, Quanguo Chen, Dingguo Wang

引用次数: 0

Tropical matrix groups and Boolean matrix groups 热带矩阵群和布尔矩阵群

IF 0.8 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications

Pub Date : 2023-12-14 DOI: 10.1142/s0219498825501671

Lin Yang, Miao-Miao Ren, Ling-Li Zeng

引用次数: 0

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