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The RFD and Kac quotients of the Hopf * -algebras of universal orthogonal quantum groups 泛正交量子群Hopf * -代数的RFD和Kac商
Annales Mathematiques Blaise Pascal Pub Date : 2020-11-30 DOI: 10.5802/ambp.402
Biswarup Das, Uwe Franz, Adam G. Skalski
{"title":"The RFD and Kac quotients of the Hopf * -algebras of universal orthogonal quantum groups","authors":"Biswarup Das, Uwe Franz, Adam G. Skalski","doi":"10.5802/ambp.402","DOIUrl":"https://doi.org/10.5802/ambp.402","url":null,"abstract":"We determine the Kac quotient and the RFD (residually finite dimensional) quotient for the Hopf *-algebras associated to universal orthogonal quantum groups.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43604767","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: 3
Injectivity radius of manifolds with a Lie structure at infinity 李氏结构流形无穷远处的注入半径
Annales Mathematiques Blaise Pascal Pub Date : 2020-10-02 DOI: 10.5802/ambp.412
Bui Quang Tu
{"title":"Injectivity radius of manifolds with a Lie structure at infinity","authors":"Bui Quang Tu","doi":"10.5802/ambp.412","DOIUrl":"https://doi.org/10.5802/ambp.412","url":null,"abstract":"Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42586434","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
Combinatoire des sous-groupes de congruence du groupe modulaire 模群同余子群的组合
Annales Mathematiques Blaise Pascal Pub Date : 2020-06-02 DOI: 10.5802/ambp.398
Flavien Mabilat
{"title":"Combinatoire des sous-groupes de congruence du groupe modulaire","authors":"Flavien Mabilat","doi":"10.5802/ambp.398","DOIUrl":"https://doi.org/10.5802/ambp.398","url":null,"abstract":"Dans cet article, on etudie la combinatoire des sous-groupes de congruence du groupe modulaire en generalisant des resultats obtenus dans le cas non modulaire. On definit pour cela une notion de solution irreductible a partir desquelles on peut construire l'ensemble des solutions. En particulier, on donne une solution particuliere, irreductible pour $N$ quelconque, et la description explicite des solutions irreductibles pour $N leq 6$.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41779089","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: 9
An L 2 -Cheeger Müller theorem on compact manifolds with boundary 带边界紧流形的l2 -Cheeger m<s:1> ller定理
Annales Mathematiques Blaise Pascal Pub Date : 2020-04-17 DOI: 10.5802/ambp.400
B. Wassermann
{"title":"An L 2 -Cheeger Müller theorem on compact manifolds with boundary","authors":"B. Wassermann","doi":"10.5802/ambp.400","DOIUrl":"https://doi.org/10.5802/ambp.400","url":null,"abstract":"We generalize a Cheeger-Muller type theorem for flat, unitary bundles on infinite covering spaces over manifolds-with-boundary, proven by Burghelea, Friedlander and Kappeller arXiv:dg-ga/9510010 [math.DG]. Employing recent anomaly results by Bruning, Ma and Zhang, we prove an analogous statement for a general flat bundle that is only required to have a unimodular restriction to the boundary.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44588524","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
Rigidity, counting and equidistribution of quaternionic Cartan chains 四元数Cartan链的刚性、计数和均匀分布
Annales Mathematiques Blaise Pascal Pub Date : 2020-02-12 DOI: 10.5802/ambp.399
Jouni Parkkonen, F. Paulin
{"title":"Rigidity, counting and equidistribution of quaternionic Cartan chains","authors":"Jouni Parkkonen, F. Paulin","doi":"10.5802/ambp.399","DOIUrl":"https://doi.org/10.5802/ambp.399","url":null,"abstract":"We prove an analog of Cartan's theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and equidistribution result for the orbits of arithmetic chains in the quaternionic Heisenberg group.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48452895","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
On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$ 关于复反射群G(d,1,n)元胞特征的一个猜想
Annales Mathematiques Blaise Pascal Pub Date : 2019-12-13 DOI: 10.5802/ambp.390
Abel Lacabanne
{"title":"On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$","authors":"Abel Lacabanne","doi":"10.5802/ambp.390","DOIUrl":"https://doi.org/10.5802/ambp.390","url":null,"abstract":"We propose a conjecture relating two different sets of characters for the complex reflection group $G(d,1,n)$. From one side, the characters are afforded by Calogero-Moser cells, a conjectural generalisation of Kazhdan-Lusztig cells for a complex reflection group. From the other side, the characters arise from a level $d$ irreducible integrable representations of $mathcal{U}_q(mathfrak{sl}_{infty})$. We prove this conjecture in some cases: in full generality for $G(d,1,2)$ and for generic parameters for $G(d,1,n)$.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75877431","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
Largeness and equational probability in groups 群体中的大与等概率
Annales Mathematiques Blaise Pascal Pub Date : 2019-09-04 DOI: 10.5802/ambp.388
Khaled K. Jaber, F. Wagner
{"title":"Largeness and equational probability in groups","authors":"Khaled K. Jaber, F. Wagner","doi":"10.5802/ambp.388","DOIUrl":"https://doi.org/10.5802/ambp.388","url":null,"abstract":"We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets. We link this with the inner measure of the set of solutions of an equation in a group, leading to new results and/or proofs in equational probabilistic group theory.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71240173","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: 3
Distribution of short sums of classical Kloosterman sums of prime powers moduli 素数幂模的经典Kloosterman和的短和分布
Annales Mathematiques Blaise Pascal Pub Date : 2019-07-03 DOI: 10.5802/ambp.385
G. Ricotta
{"title":"Distribution of short sums of classical Kloosterman sums of prime powers moduli","authors":"G. Ricotta","doi":"10.5802/ambp.385","DOIUrl":"https://doi.org/10.5802/ambp.385","url":null,"abstract":"Corentin Perret-Gentil proved, under some very general conditions, that short sums of $ell$-adic trace functions over finite fields of varying center converges in law to a Gaussian random variable or vector. The main inputs are P.~Deligne's equidistribution theorem, N.~Katz' works and the results surveyed in cite{MR3338119}. In particular, this applies to $2$-dimensional Kloosterman sums $mathsf{Kl}_{2,mathbb{F}_q}$ studied by N.~Katz in cite{MR955052} and in cite{MR1081536} when the field $mathbb{F}_q$ gets large. par This article considers the case of short sums of normalized classical Kloosterman sums of prime powers moduli $mathsf{Kl}_{p^n}$, as $p$ tends to infinity among the prime numbers and $ngeq 2$ is a fixed integer. A convergence in law towards a real-valued standard Gaussian random variable is proved under some very natural conditions.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46364299","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
Averages and the $ell ^{q,1}$ cohomology of Heisenberg groups Heisenberg群的平均值和$ell ^{q,1}$上同调
Annales Mathematiques Blaise Pascal Pub Date : 2019-04-12 DOI: 10.5802/ambp.384
P. Pansu, F. Tripaldi
{"title":"Averages and the $ell ^{q,1}$ cohomology of Heisenberg groups","authors":"P. Pansu, F. Tripaldi","doi":"10.5802/ambp.384","DOIUrl":"https://doi.org/10.5802/ambp.384","url":null,"abstract":"Averages are invariants defined on the $ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $ell^1$ cohomology vanishes in these cases.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45514304","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: 10
Finiteness of the image of the Reidemeister torsion of a splice 拼接的瑞德米斯特扭转像的有限性
Annales Mathematiques Blaise Pascal Pub Date : 2019-04-04 DOI: 10.5802/ambp.389
Teruaki Kitano, Yuta Nozaki
{"title":"Finiteness of the image of the Reidemeister torsion of a splice","authors":"Teruaki Kitano, Yuta Nozaki","doi":"10.5802/ambp.389","DOIUrl":"https://doi.org/10.5802/ambp.389","url":null,"abstract":"The set $mathit{RT}(M)$ of values of the $mathit{SL}(2,mathbb{C})$-Reidemeister torsion of a 3-manifold $M$ can be both finite and infinite. We prove that $mathit{RT}(M)$ is a finite set if $M$ is the splice of two certain knots in the 3-sphere. The proof is based on an observation on the character varieties and $A$-polynomials of knots.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42149291","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: 3
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