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Int. J. Algebra Comput.最新文献

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Finite groups satisfying the independence property 满足独立性的有限群
Pub Date : 2022-08-08 DOI: 10.1142/S021819672350025X
S. D. Freedman, A. Lucchini, Daniele Nemmi, C. Roney-Dougal
We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either ${x,y}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other. We give a complete classification of the finite groups with this property, and in particular prove that every such group is supersoluble. A key ingredient of our proof is a theorem showing that all but three finite almost simple groups $H$ contain an element $s$ such that the maximal subgroups of $H$ containing $s$, but not containing the socle of $H$, are pairwise non-conjugate.
我们说一个有限群$G$满足独立性,如果对于$G$的每一对不同的元素$x$和$y$, ${x,y}$包含在$G$的最小生成集中,或者$x$和$y$中的一个是另一个的幂。我们给出了具有这一性质的有限群的一个完全分类,并特别证明了每一个这样的群都是超溶的。我们证明的一个关键成分是一个定理,证明除了三个有限几乎单群$H$以外的所有群$H$都包含一个元素$s$,使得$H$的极大子群包含$s$,但不包含$H$的集合,是成对非共轭的。
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引用次数: 2
Classifying Nichols algebras over classical Weyl groups 经典Weyl群上Nichols代数的分类
Pub Date : 2022-07-29 DOI: 10.1142/s021819672250062x
Weicai Wu, Panyue Zhou
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引用次数: 0
Abstract key polynomials and MacLane-Vaquié chains 摘要关键多项式和maclane - vaqui<e:1>链
Pub Date : 2022-07-16 DOI: 10.1142/s0218196723500030
Sneha Mavi, Anuj Bishnoi
In this paper, for a valued field $(K, v)$ of arbitrary rank and an extension $w$ of $v$ to $K(X),$ a relation between induced complete sequences of abstract key polynomials and MacLane-Vaqui'e chains is given.
对于任意秩的值域$(K, v)$和$v$到$K(X)的扩展$w$,给出了抽象键多项式的诱导完全序列与MacLane-Vaqui链之间的关系。
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引用次数: 0
Semiprime Novikov algebras
Pub Date : 2022-06-09 DOI: 10.1142/S0218196722500606
A. Panasenko
. We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (semi)prime algebra is (semi)prime algebra. We proved this statement for Novikov algebras. It implies that a Baer radical exists in a class of Novikov algebras. Also, we proved that a minimal ideal of Novikov algebra is either trivial, or a simple algebra.
。我们学习素数和半素数Novikov代数。证明了素数非结合诺维科夫代数具有零核和零中心。众所周知,一个可选的半素数代数的理想是半素数代数。我们用诺维科夫代数证明了这个命题。证明了一类Novikov代数中存在Baer根。同时,我们证明了Novikov代数的极小理想要么是平凡代数,要么是简单代数。
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引用次数: 3
The order of the unitary subgroups of group algebras 群代数的酉子群的阶
Pub Date : 2022-06-05 DOI: 10.1142/s0218196722500576
Z. Balogh
Let F G be the group algebra of a finite p -group G over a finite field F of positive characteristic p . Let ⊛ be an involution of the algebra F G which is a linear extension of an anti-automorphism of the group G to F G . If p is an odd prime, then the order of the ⊛ -unitary subgroup of F G is established. For the case p = 2 we generalize a result obtained for finite abelian 2-groups. It is proved that the order of the ∗ -unitary subgroup of F G of a non-abelian 2-group is always divisible by a number which depends only on the size of F , the order of G and the number of elements of order two in G . Moreover, we show that the order of the ∗ -unitary subgroup of F G determines the order of the finite p -group G .
设F G是有限p群G在有限域F上的正特征p的群代数。设是代数F G的一个对合,它是群G对F G的一个反自同构的线性扩展。如果p是奇素数,则建立了F G的 -酉子群的阶。对于p = 2的情况,我们推广了有限阿贝尔2群的一个结果。证明了非阿贝尔2-群的F G的* -酉子群的阶总是可被一个数整除,该数仅与F的大小、G的阶和G中2阶元素的个数有关。此外,我们证明了F G的*酉子群的阶决定了有限p群G的阶。
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引用次数: 0
*-Graded Capelli polynomials and their asymptotics *-分阶Capelli多项式及其渐近性
Pub Date : 2022-05-20 DOI: 10.1142/s0218196722500503
F. Benanti, A. Valenti
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引用次数: 0
Derivation problem for quandle algebras 纠缠代数的导数问题
Pub Date : 2022-05-18 DOI: 10.1142/s0218196722500424
M. Elhamdadi, A. Makhlouf, S. Silvestrov, E. Zappala
The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.
摘要本文的目的是引入并研究纠缠代数的导数概念。更准确地说,我们描述了结构常数上的对称性,为线性映射的导数提供了表征。我们得到了特征为零的二面体四角群的四角代数的导数的完整刻划,并给出了导数的李代数的维数。给出了许多关于零特征和正特征的显式例子和计算。此外,我们研究了非结合结构在Schafer意义上的内推导。我们得到了亚历山大群的群群代数的李变换代数的必要条件,并给出了在低维上的显式计算。
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引用次数: 3
Finite basis problem for Catalan monoids with involution 具有对合的Catalan一元群的有限基问题
Pub Date : 2022-05-10 DOI: 10.1142/s0218196722500497
Meng Gao, Wen Ting Zhang, Yanfeng Luo
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引用次数: 1
Rigidity results for Lie algebras admitting a post-Lie algebra structure 承认后李代数结构的李代数的刚性结果
Pub Date : 2022-05-09 DOI: 10.1142/s0218196722500679
D. Burde, K. Dekimpe, Mina Monadjem
We study rigidity questions for pairs of Lie algebras $(mathfrak{g},mathfrak{n})$ admitting a post-Lie algebra structure. We show that if $mathfrak{g}$ is semisimple and $mathfrak{n}$ is arbitrary, then we have rigidity in the sense that $mathfrak{g}$ and $mathfrak{n}$ must be isomorphic. The proof uses a result on the decomposition of a Lie algebra $mathfrak{g}=mathfrak{s}_1dotplus mathfrak{s}_2$ as the direct vector space sum of two semisimple subalgebras. We show that $mathfrak{g}$ must be semisimple and hence isomorphic to the direct Lie algebra sum $mathfrak{g}cong mathfrak{s}_1oplus mathfrak{s}_2$. This solves some open existence questions for post-Lie algebra structures on pairs of Lie algebras $(mathfrak{g},mathfrak{n})$. We prove additional existence results for pairs $(mathfrak{g},mathfrak{n})$, where $mathfrak{g}$ is complete, and for pairs, where $mathfrak{g}$ is reductive with $1$-dimensional center and $mathfrak{n}$ is solvable or nilpotent.
研究了承认后李代数结构的李代数对$(mathfrak{g},mathfrak{n})$的刚性问题。我们证明,如果$mathfrak{g}$是半简单的,$mathfrak{n}$是任意的,那么我们在$mathfrak{g}$和$mathfrak{n}$必须同构的意义上具有刚性。证明使用李代数$mathfrak{g}=mathfrak{s}_1dotplus mathfrak{s}_2$分解的结果作为两个半简单子代数的直接向量空间和。我们证明$mathfrak{g}$必须是半简单的,因此与直接李代数和$mathfrak{g}cong mathfrak{s}_1oplus mathfrak{s}_2$同构。这解决了李代数对上后李代数结构的一些开放存在性问题$(mathfrak{g},mathfrak{n})$。我们证明了对$(mathfrak{g},mathfrak{n})$的附加存在性结果,其中$mathfrak{g}$是完全的,对$mathfrak{g}$是约化的,以$1$为中心,$mathfrak{n}$是可解的或幂零的。
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引用次数: 1
Extremal Betti numbers of symbolic powers of two-dimensional squarefree monomial ideals 二维无平方单项式理想的符号幂的极值贝蒂数
Pub Date : 2022-05-06 DOI: 10.1142/s0218196722500448
Nguyên Quang Lôc, N. Minh, P. Thuy
Let [Formula: see text] be a two-dimensional squarefree monomial ideal in a polynomial ring [Formula: see text], where [Formula: see text] is a field. In this paper, we give explicit formulas for the extremal Betti numbers of the [Formula: see text]th symbolic power of [Formula: see text] for all [Formula: see text]. As a consequence, we characterize the rings [Formula: see text] which are pseudo-Gorenstein as sense of Ene et al. [Pseudo-Gorenstein and level Hibi rings, J. Algebra 431 (2015) 138–161]. We also provide a complete classification for the level property of the second symbolic power [Formula: see text]. In particular, we obtain a new algebraic-property of the unknown Moore graph of degree 57.
设[公式:见文]是多项式环中的二维无平方单项式理想[公式:见文],其中[公式:见文]是一个域。本文给出了所有[公式:见文]的[公式:见文]的[公式:见文]的[符号幂]的极值贝蒂数的显式公式。因此,我们将伪gorenstein环表征为Ene等人的意义[伪gorenstein和水平Hibi环,J.代数431(2015)138-161]。我们还对第二符号幂的层次属性提供了一个完整的分类[公式:见文]。特别地,我们得到了未知的57次摩尔图的一个新的代数性质。
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引用次数: 0
期刊
Int. J. Algebra Comput.
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