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Journal of Combinatorial Algebra最新文献

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The algebra of Boolean matrices, correspondence functors, and simplicity 布尔矩阵代数、对应函子和简单性
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2019-02-13 DOI: 10.4171/jca/44
S. Bouc, Jacques Th'evenaz
{"title":"The algebra of Boolean matrices, correspondence functors, and simplicity","authors":"S. Bouc, Jacques Th'evenaz","doi":"10.4171/jca/44","DOIUrl":"https://doi.org/10.4171/jca/44","url":null,"abstract":"We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence functor. The method uses the theory of such functors developed in [BT2, BT3], as well as some new ingredients in the theory of finite lattices.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49191939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 11
Negative curvature in automorphism groups of one-ended hyperbolic groups 单端双曲群的自同构群中的负曲率
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-10-24 DOI: 10.4171/jca/33
A. Genevois
{"title":"Negative curvature in automorphism groups of one-ended hyperbolic groups","authors":"A. Genevois","doi":"10.4171/jca/33","DOIUrl":"https://doi.org/10.4171/jca/33","url":null,"abstract":"In this article, we show that some negative curvature may survive when taking the automorphism group of a finitely generated group. More precisely, we prove that the automorphism group $mathrm{Aut}(G)$ of a one-ended hyperbolic group $G$ turns out to be acylindrically hyperbolic. As a consequence, given a group $H$ and a morphism $varphi : H to mathrm{Aut}(G)$, we deduce that the semidirect product $G rtimes_varphi H$ is acylindrically hyperbolic if and only if $mathrm{ker}(H overset{varphi}{to} mathrm{Aut}(G) to mathrm{Out}(G))$ is finite.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41965973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 4
The isoperimetric spectrum of finitely presented groups 有限存在群的等周谱
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-08-17 DOI: 10.4171/JCA/2-4-2
M. Sapir
{"title":"The isoperimetric spectrum of finitely presented groups","authors":"M. Sapir","doi":"10.4171/JCA/2-4-2","DOIUrl":"https://doi.org/10.4171/JCA/2-4-2","url":null,"abstract":"The isoperimeric spectrum consists of all real positive numbers $alpha$ such that $O(n^alpha)$ is the Dehn function of a finitely presented group. In this note we show how a recent result of Olshanskii completes the description of the isoperimetric spectrum modulo the celebrated Computer Science conjecture (and one of the seven Millennium Problems) $mathbf{P=NP}$ and even a formally weaker conjecture.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JCA/2-4-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49476555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1
Affine hyperplane arrangements and Jordan classes 仿射超平面排列与Jordan类
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-07-27 DOI: 10.4171/jca/48
G. Carnovale, F. Esposito
{"title":"Affine hyperplane arrangements and Jordan classes","authors":"G. Carnovale, F. Esposito","doi":"10.4171/jca/48","DOIUrl":"https://doi.org/10.4171/jca/48","url":null,"abstract":"We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49492241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
Khovanskii-finite valuations, rational curves, and torus actions khovanski -有限值，有理曲线和环面作用
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-07-23 DOI: 10.4171/jca/41
N. Ilten, Milena Wrobel
{"title":"Khovanskii-finite valuations, rational curves, and torus actions","authors":"N. Ilten, Milena Wrobel","doi":"10.4171/jca/41","DOIUrl":"https://doi.org/10.4171/jca/41","url":null,"abstract":"We study full rank homogeneous valuations on (multi)-graded domains and ask when they have finite Khovanskii bases. We show that there is a natural reduction from multigraded to simply graded domains. As special cases, we consider projective coordinate rings of rational curves, and almost toric varieties. Our results relate to several problems posed by Kaveh and Manon, and imply that the procedure of Bossinger-Lamboglia-Mincheva-Mohammadi for producing tropical prime cones will not terminate in general.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41247372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 9
Non-kissing and non-crossing complexes for locally gentle algebras 局部温和代数的非亲和非交叉配合物
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-07-12 DOI: 10.4171/jca/35
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
{"title":"Non-kissing and non-crossing complexes for locally gentle algebras","authors":"Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon","doi":"10.4171/jca/35","DOIUrl":"https://doi.org/10.4171/jca/35","url":null,"abstract":"Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, oriented surface with boundary, endowed with a pair of dual dissections. From those geometric data, we define two simplicial complexes: the accordion complex, and the slalom complex, generalizing work of A. Garver and T. McConville in the case of a disk. We show that all three simplicial complexes are isomorphic, and that they are pure and thin. In particular, there is a notion of mutation on their facets, akin to $tau$-tilting mutation. Along the way, we also construct inverse bijections between the set of isomorphism classes of locally gentle bound quivers and the set of homeomorphism classes of punctured, marked, oriented surfaces with boundary, endowed with a pair of dual dissections.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73594277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 31
Drinfeld double of quantum groups, tilting modules and $mathbb Z$-modular data associated to complex reflection groups 量子群的Drinfeld二重、倾斜模和与复反射群相关的$mathbb Z$模数据
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-07-02 DOI: 10.4171/JCA/45
Abel Lacabanne
{"title":"Drinfeld double of quantum groups, tilting modules and $mathbb Z$-modular data associated to complex reflection groups","authors":"Abel Lacabanne","doi":"10.4171/JCA/45","DOIUrl":"https://doi.org/10.4171/JCA/45","url":null,"abstract":"Generalizing Lusztig's work, Malle as associated to any imprimitive complex reflection $W$ group a set of \"unipotent characters\", which are in bijection of the usual unipotent characters of the associated finite reductive group if $W$ is a Weyl group. He also obtained a partition of these characters into families and associated to each family a $mathbb{Z}$-modular datum. We construct a categorification of some of these data, by studying the category of tilting modules of the Drinfeld double of the quantum enveloping algebra of the Borel of a simple complex Lie algebra.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44809390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 6
On the complexity of the cogrowth sequence 关于共生序列的复杂性
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-05-21 DOI: 10.4171/jca/39
J. Bell, M. Mishna
{"title":"On the complexity of the cogrowth sequence","authors":"J. Bell, M. Mishna","doi":"10.4171/jca/39","DOIUrl":"https://doi.org/10.4171/jca/39","url":null,"abstract":"Given a finitely generated group with generating set $S$, we study the cogrowth sequence, which is the number of words of length $n$ over the alphabet $S$ that are equal to one. This is related to the probability of return for walks in a Cayley graph with steps from $S$. We prove that the cogrowth sequence is not P-recursive when $G$ is an amenable group of superpolynomial growth, answering a question of Garrabant and Pak. In addition, we compute the cogrowth for certain infinite families of free products of finite groups and free groups, and prove that a gap theorem holds: if $S$ is a finite symmetric generating set for a group $G$ and if $a_n$ denotes the number of words of length $n$ over the alphabet $S$ that are equal to $1$ then either $limsup_n a_n^{1/n} le 2$ or $limsup_n a_n^{1/n} ge 2sqrt{2}$.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/jca/39","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47096979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements 对称单复形、$G$-半拟阵和阿贝尔排列的Stanley–Reisner环
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-04-19 DOI: 10.4171/JCA/53
Alessio D'Alì, Emanuele Delucchi
{"title":"Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements","authors":"Alessio D'Alì, Emanuele Delucchi","doi":"10.4171/JCA/53","DOIUrl":"https://doi.org/10.4171/JCA/53","url":null,"abstract":"We extend the notion of face rings of simplicial complexes and simplicial posets to the case of finite-length simplicial posets with a group action. The action on the complex induces an action on the face ring, and we prove that the ring of invariants is isomorphic to the face ring of the quotient simplicial poset when the group action is translative (in the sense of Delucchi-Riedel). When the acted-upon poset is the independence complex of a semimatroid, the h-polynomial of the ring of invariants can be read off the Tutte polynomial of the associated G-semimatroid. We thus recover the classical theory in the case of trivial group actions on finite simplicial posets and, in the special case of central toric arrangements, our rings are isomorphic to those defined by Martino and by Lenz. We also describe a further condition on the group action ensuring that the topological Cohen-Macaulay property is preserved under quotients. In particular, we prove that the independence complex and the Stanley-Reisner ring of any Abelian arrangement are Cohen-Macaulay over every field. As a byproduct, we prove that posets of connected components (also known as posets of layers) of Abelian arrangements are (homotopically) Cohen-Macaulay.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 7
Formations of finite groups with the M. Hall property 具有M. Hall性质的有限群的形成
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2018-03-13 DOI: 10.4171/JCA/28
K. Auinger, Alexander Bors
{"title":"Formations of finite groups with the M. Hall property","authors":"K. Auinger, Alexander Bors","doi":"10.4171/JCA/28","DOIUrl":"https://doi.org/10.4171/JCA/28","url":null,"abstract":"The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous (and therefore Hall) but not locally extensible are constructed. Some open questions are also mentioned.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JCA/28","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48436794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
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