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On well-rounded lattices and lower bounds for the minimum norm of ideal lattices 关于圆角格和理想格的最小范数的下界
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-29 DOI: 10.1007/s00013-024-02065-y
Carina Alves, João E. Strapasson, Robson R. de Araujo
{"title":"On well-rounded lattices and lower bounds for the minimum norm of ideal lattices","authors":"Carina Alves,&nbsp;João E. Strapasson,&nbsp;Robson R. de Araujo","doi":"10.1007/s00013-024-02065-y","DOIUrl":"10.1007/s00013-024-02065-y","url":null,"abstract":"<div><p>In this paper, we study properties of well-rounded ideal lattices focusing on the lower bounds for their minimum norm. We present counterexamples showing that the stated bounds in a previous work do not hold for mixed number fields through the canonical embedding. However, we prove that ideal lattices obtained via the Minkowski embedding (instead of the canonical embedding) are well-rounded if and only if the number field is cyclotomic. Additionally, we derive new lower bounds for the minimum norm of ideal lattices under both the canonical and twisted embeddings. Our results not only refine existing theories but also open new possibilities for research on well-rounded ideal lattices in higher dimensions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"121 - 130"},"PeriodicalIF":0.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Irreducible (Y(mathfrak {gl}_2))-modules arising from free modules 由自由模块产生的不可还原的 (Y(mathfrak {gl}_2))-模块
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-28 DOI: 10.1007/s00013-024-02068-9
Han Dai, Dashu Xu
{"title":"Irreducible (Y(mathfrak {gl}_2))-modules arising from free modules","authors":"Han Dai,&nbsp;Dashu Xu","doi":"10.1007/s00013-024-02068-9","DOIUrl":"10.1007/s00013-024-02068-9","url":null,"abstract":"<div><p>We classify a class of modules for the Yangian <span>(Y(mathfrak {gl}_2))</span>, where the element <span>(e_{21}in Y(mathfrak {gl}_2))</span> acts regularly. These modules can be realized by use of the differential operators. Moreover, we compute the central characters of these modules by employing the trick of formal generating series.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"605 - 613"},"PeriodicalIF":0.5,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Approximation of classes of Poisson integrals by incomplete Fejér means 更正：用不完全费热法逼近泊松积分的类别
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-28 DOI: 10.1007/s00013-024-02064-z
Olga Rovenska
{"title":"Correction to: Approximation of classes of Poisson integrals by incomplete Fejér means","authors":"Olga Rovenska","doi":"10.1007/s00013-024-02064-z","DOIUrl":"10.1007/s00013-024-02064-z","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"679 - 680"},"PeriodicalIF":0.5,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Tracing the orbitals of the quantum permutation group 更正：追踪量子排列组合的轨道
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-28 DOI: 10.1007/s00013-024-02056-z
J.P. McCarthy
{"title":"Correction to: Tracing the orbitals of the quantum permutation group","authors":"J.P. McCarthy","doi":"10.1007/s00013-024-02056-z","DOIUrl":"10.1007/s00013-024-02056-z","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"681 - 682"},"PeriodicalIF":0.5,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Noetherian criterion for sequences of modules 模序列的noether判据
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-25 DOI: 10.1007/s00013-024-02066-x
Wee Liang Gan, Khoa Ta
{"title":"A Noetherian criterion for sequences of modules","authors":"Wee Liang Gan,&nbsp;Khoa Ta","doi":"10.1007/s00013-024-02066-x","DOIUrl":"10.1007/s00013-024-02066-x","url":null,"abstract":"<div><p>We prove a Noetherian criterion for a sequence of modules with linear maps between them. This generalizes a Noetherian criterion of Gan and Li for infinite EI categories. We apply our criterion to the linear categories associated to certain diagram algebras defined by Patzt.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"131 - 136"},"PeriodicalIF":0.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Leavitt path algebras of quantum quivers 量子颤振的莱维特路径代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-25 DOI: 10.1007/s00013-024-02067-w
Joshua Graham, Rishabh Goswami, Jason Palin
{"title":"Leavitt path algebras of quantum quivers","authors":"Joshua Graham,&nbsp;Rishabh Goswami,&nbsp;Jason Palin","doi":"10.1007/s00013-024-02067-w","DOIUrl":"10.1007/s00013-024-02067-w","url":null,"abstract":"<div><p>Adapting a recent work of Brannan et al. on extending graph <span>(C^*)</span>-algebras to quantum graphs, we introduce “Quantum Quivers” as an analogue of quivers where the edge and vertex set has been replaced by a <span>(C^*)</span>-algebra and the maps between the sets by <span>(*)</span>-homomorphisms. Additionally, we develop the theory around these structures and construct a notion of Leavitt path algebra over them and also compute the monoid of finitely generated projective modules over this class of algebras.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"29 - 48"},"PeriodicalIF":0.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Kimoto–Wakayama supercongruence conjecture on Apéry-like numbers 关于阿佩里样数上的木户-和歌山超共格猜想
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-25 DOI: 10.1007/s00013-024-02062-1
Ji-Cai Liu
{"title":"On the Kimoto–Wakayama supercongruence conjecture on Apéry-like numbers","authors":"Ji-Cai Liu","doi":"10.1007/s00013-024-02062-1","DOIUrl":"10.1007/s00013-024-02062-1","url":null,"abstract":"<div><p>Kimoto and Wakayama [Ann. Inst. Henri Poincaré D 10 (2023), 205–275] studied the special values of the spectral zeta function <span>(zeta _Q(s))</span> associated to the non-commutative harmonic oscillator <span>(Q_{alpha ,beta })</span>. Two kinds of Apéry-like numbers (even case <span>(widetilde{J}_{2s+2}(n))</span> and odd case <span>(widetilde{J}_{2s+1}(n))</span>) naturally arise in the expressions for the special values of <span>(zeta _Q(s))</span> at integer points. Supercongruences among these Apéry-like numbers lead one to the modularity of the generating functions of the Apéry-like numbers. Kimoto and Wakayama established a supercongruence among <span>(widetilde{J}_{2s+2}(n))</span>, and conjectured the same type of supercongruence for <span>(widetilde{J}_{2s+1}(n))</span> as in the even case <span>(widetilde{J}_{2s+2}(n))</span>. In this work, we confirm Kimoto and Wakayama’s supercongruence conjecture in the odd case of Apéry-like numbers <span>(widetilde{J}_{2s+1}(n))</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"615 - 624"},"PeriodicalIF":0.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Injective generation of the derived category and finitistic dimension conjecture 派生范畴的注入生成和有限维度猜想
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-09 DOI: 10.1007/s00013-024-02053-2
Hossein Eshraghi, Ali Hajizamani
{"title":"Injective generation of the derived category and finitistic dimension conjecture","authors":"Hossein Eshraghi,&nbsp;Ali Hajizamani","doi":"10.1007/s00013-024-02053-2","DOIUrl":"10.1007/s00013-024-02053-2","url":null,"abstract":"<div><p>For a finite dimensional algebra <span>(Lambda )</span>, the problem of whether the unbounded derived category <span>(mathbb {D}(Lambda ))</span> is equal to its localizing subcategory generated by injective <span>(Lambda )</span>-modules was firstly considered by Keller in 2001. If this happens to be true, it is usually said that injectives generate for <span>(Lambda )</span>. Some connections to famous homological conjectures were illuminated by Keller himself. Recently, Rickard presented several classes of rings, including particular types of finite dimensional algebras as well as commutative Noetherian rings, for which injectives generate. He also proved that if injectives generate for <span>(Lambda )</span>, then it satisfies the big finitistic dimension conjecture. The main objective of this paper is to discuss when the reverse statement also holds. We show that, under some mild condition, the injective generation phenomenon and the big finitistic dimension conjecture for <span>(Lambda )</span> are equivalent.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"593 - 604"},"PeriodicalIF":0.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A topology on the Fremlin tensor product of locally convex-solid vector lattices 局部凸固向量网格的弗雷姆林张量积拓扑学
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-01 DOI: 10.1007/s00013-024-02055-0
Omid Zabeti
{"title":"A topology on the Fremlin tensor product of locally convex-solid vector lattices","authors":"Omid Zabeti","doi":"10.1007/s00013-024-02055-0","DOIUrl":"10.1007/s00013-024-02055-0","url":null,"abstract":"<div><p>Suppose that <i>E</i> and <i>F</i> are Banach lattices. It is known that there are several norms on the Fremlin tensor product <span>(E{overline{otimes }} F)</span> that turn it into a normed lattice; in particular, the projective norm <span>(|pi |)</span> (known as the Fremlin projective norm) and the injective norm <span>(|epsilon |)</span> (known as the Wittstock injective norm). Now, assume that <i>E</i> and <i>F</i> are locally convex-solid vector lattices. Although we have a suitable vector lattice structure for the tensor product <i>E</i> and <i>F</i> (known as the Fremlin tensor product and denoted by <span>(E{overline{otimes }}F)</span>), there is a lack of topological structure on <span>(E{overline{otimes }}F)</span>, in general. In this note, we consider a linear topology on <span>(E{overline{otimes }}F)</span> that makes it into a locally convex-solid vector lattice, as well; this approach can be taken as a generalization of the projective norm of the Fremlin tensor product between Banach lattices.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"625 - 633"},"PeriodicalIF":0.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A classification of generalized root systems 通用根系的分类
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-01 DOI: 10.1007/s00013-024-02046-1
Michael Cuntz, Bernhard Mühlherr
{"title":"A classification of generalized root systems","authors":"Michael Cuntz,&nbsp;Bernhard Mühlherr","doi":"10.1007/s00013-024-02046-1","DOIUrl":"10.1007/s00013-024-02046-1","url":null,"abstract":"<div><p>Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a Euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note, we prove the conjecture and provide a complete classification of generalized root systems up to equivalence.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"567 - 583"},"PeriodicalIF":0.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02046-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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