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Communications in Mathematics最新文献

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Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1, 1 mid m)$ and nilindex $n+m$ 零根具有特征序列$(n- 1,1 m)$和零索引$n+m$的可解莱布尼兹超代数
Communications in Mathematics Pub Date : 2023-09-20 DOI: 10.46298/cm.11369
Khudoyberdiyev A. Kh., Muratova Kh. A
{"title":"Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1, 1 mid m)$ and nilindex $n+m$","authors":"Khudoyberdiyev A. Kh., Muratova Kh. A","doi":"10.46298/cm.11369","DOIUrl":"https://doi.org/10.46298/cm.11369","url":null,"abstract":"Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 | m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable Leibniz superalgebras whose nilradical is a nilpotent Leibniz superalgebra with nilindex $n + m$ and characteristic sequence $(n-1, 1 | m)$. We obtain a condition for the value of parameters of the classes of such nilpotent superalgebras for which they have a solvable extension. Moreover, the classification of solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with the maximal nilindex is given.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over K"ahlerian manifold 关于K“ahlerian流形上Berger型变形Sasaki度量余切丛的测地线的注记
Communications in Mathematics Pub Date : 2023-09-03 DOI: 10.46298/cm.11025
A. Zagane
{"title":"Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over K\"ahlerian manifold","authors":"A. Zagane","doi":"10.46298/cm.11025","DOIUrl":"https://doi.org/10.46298/cm.11025","url":null,"abstract":"In this paper, first, we introduce the Berger-type deformed Sasaki metric on\u0000the cotangent bundle $T^{ast}M$ over a K\"{a}hlerian manifold $(M^{2m}, J, g)$\u0000and investigate the Levi-Civita connection of this metric. Secondly, we present\u0000the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and\u0000we investigate the Levi-Civita connection. Finally, we study the geodesics on\u0000the cotangent bundle and on unit cotangent bundle with respect to the\u0000Berger-type deformed Sasaki metric.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47291270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noncommutative Algebra and Representation Theory: Symmetry, Structure & Invariants 非交换代数与表示理论》：对称、结构与不变式
Communications in Mathematics Pub Date : 2023-07-31 DOI: 10.46298/cm.11678
S. A. Lopes
{"title":"Noncommutative Algebra and Representation Theory: Symmetry, Structure & Invariants","authors":"S. A. Lopes","doi":"10.46298/cm.11678","DOIUrl":"https://doi.org/10.46298/cm.11678","url":null,"abstract":"This is an abridged version of our Habilitation thesis. In these notes, we aim to summarize our research interests and achievements as well as motivate what drives our work: symmetry, structure and invariants. The paradigmatic example which permeates and often inspires our research is the Weyl algebra $mathbb{A}_{1}$.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139353090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The integer point transform as a complete invariant 作为完全不变量的整数点变换
Communications in Mathematics Pub Date : 2023-04-18 DOI: 10.46298/cm.11218
S. Robins
{"title":"The integer point transform as a complete invariant","authors":"S. Robins","doi":"10.46298/cm.11218","DOIUrl":"https://doi.org/10.46298/cm.11218","url":null,"abstract":"The integer point transform $sigma_PP$ is an important invariant of a\u0000rational polytope $PP$, and here we show that it is a complete invariant. We\u0000prove that it is only necessary to evaluate $sigma_PP$ at one algebraic point\u0000in order to uniquely determine $PP$, by employing the Lindemann-Weierstrass\u0000theorem. Similarly, we prove that it is only necessary to evaluate the Fourier\u0000transform of a rational polytope $PP$ at a single algebraic point, in order to\u0000uniquely determine $PP$. We prove that identical uniqueness results also hold\u0000for integer cones.\u0000 In addition, by relating the integer point transform to finite Fourier\u0000transforms, we show that a finite number of emph{integer point evaluations} of\u0000$sigma_PP$ suffice in order to uniquely determine $PP$. We also give an\u0000equivalent condition for central symmetry of a finite point set, in terms of\u0000the integer point transform, and prove some facts about its local maxima. Most\u0000of the results are proven for arbitrary finite sets of integer points in\u0000$R^d$.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42669958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Discrete complex reflection groups 离散复反射群
Communications in Mathematics Pub Date : 2023-04-18 DOI: 10.46298/cm.11249
V. Popov
{"title":"Discrete complex reflection groups","authors":"V. Popov","doi":"10.46298/cm.11249","DOIUrl":"https://doi.org/10.46298/cm.11249","url":null,"abstract":"Here are reproduced slightly edited notes of my lectures on the\u0000classification of discrete groups generated by complex reflections of Hermitian\u0000affine spaces delivered in October of 1980 at the University of Utrecht.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46780822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
A recursive formula for the product of element orders of finite abelian groups 有限阿贝尔群元素阶积的递推公式
Communications in Mathematics Pub Date : 2023-04-04 DOI: 10.46298/cm.10996
Subhrajyoti Saha
{"title":"A recursive formula for the product of element orders of finite abelian groups","authors":"Subhrajyoti Saha","doi":"10.46298/cm.10996","DOIUrl":"https://doi.org/10.46298/cm.10996","url":null,"abstract":"Let G be a finite group and let ψ(G) denote the sum of element orders of G; later this concept has been used to define R(G) which is the product of the element orders of G. Motivated by the recursive formula for ψ(G), we consider a finite abelian group G and obtain a similar formula for R(G).","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44276178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix formulas for multiplicities in the spin module 自旋模中乘法的矩阵公式
Communications in Mathematics Pub Date : 2023-04-04 DOI: 10.46298/cm.11156
Lucas Fresse, S. Mehdi
{"title":"Matrix formulas for multiplicities in the spin module","authors":"Lucas Fresse, S. Mehdi","doi":"10.46298/cm.11156","DOIUrl":"https://doi.org/10.46298/cm.11156","url":null,"abstract":"We obtain inductive and enumerative formulas for the multiplicities of the\u0000weights of the spin module for the Clifford algebra of a Levi subalgebra in a\u0000complex semisimple Lie algebra. Our formulas involve only matrices and\u0000tableaux, and our techniques combine linear algebra, Lie theory, and\u0000combinatorics. Moreover, this suggests a relationship with complex nilpotent\u0000orbits. The case of the special linear Lie algebra $mathfrak{sl}(n,{mathbb\u0000C})$ is emphasized.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49449176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minkowski's successive minima in convex and discrete geometry 凸和离散几何中的Minkowski连续极小
Communications in Mathematics Pub Date : 2023-03-31 DOI: 10.46298/cm.11155
I. Aliev, M. Henk
{"title":"Minkowski's successive minima in convex and discrete geometry","authors":"I. Aliev, M. Henk","doi":"10.46298/cm.11155","DOIUrl":"https://doi.org/10.46298/cm.11155","url":null,"abstract":"In this short survey we want to present some of the impact of Minkowski's\u0000successive minima within Convex and Discrete Geometry. Originally related to\u0000the volume of an $o$-symmetric convex body, we point out relations of the\u0000successive minima to other functionals, as e.g., the lattice point enumerator\u0000or the intrinsic volumes and we present some old and new conjectures about\u0000them. Additionally, we discuss an application of successive minima to a version\u0000of Siegel's lemma.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49090055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Perfect Copositive Matrices 完全共生矩阵
Communications in Mathematics Pub Date : 2023-03-30 DOI: 10.46298/cm.11141
Valentin Dannenberg, Achill Schurmann
{"title":"Perfect Copositive Matrices","authors":"Valentin Dannenberg, Achill Schurmann","doi":"10.46298/cm.11141","DOIUrl":"https://doi.org/10.46298/cm.11141","url":null,"abstract":"In this paper we give a first study of perfect copositive $n times n$\u0000matrices. They can be used to find rational certificates for completely\u0000positive matrices. We describe similarities and differences to classical\u0000perfect, positive definite matrices. Most of the differences occur only for $n\u0000geq 3$, where we find for instance lower rank and indefinite perfect matrices.\u0000Nevertheless, we find for all $n$ that for every classical perfect matrix there\u0000is an arithmetically equivalent one which is also perfect copositive.\u0000Furthermore we study the neighborhood graph and polyhedral structure of perfect\u0000copositive matrices. As an application we obtain a new characterization of the\u0000cone of completely positive matrices: It is equal to the set of nonnegative\u0000matrices having a nonnegative inner product with all perfect copositive\u0000matrices.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48474532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On triviality of uniform Diophantine exponents of lattices 格的一致丢番图指数的平凡性
Communications in Mathematics Pub Date : 2023-03-29 DOI: 10.46298/cm.11137
O. German
{"title":"On triviality of uniform Diophantine exponents of lattices","authors":"O. German","doi":"10.46298/cm.11137","DOIUrl":"https://doi.org/10.46298/cm.11137","url":null,"abstract":"In this paper we prove that uniform Diophantine exponents of lattices attain\u0000only trivial values.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46522794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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