We determine the Kac quotient and the RFD (residually finite dimensional) quotient for the Hopf *-algebras associated to universal orthogonal quantum groups.
我们确定了与泛正交量子群相关的Hopf *-代数的Kac商和RFD商。
{"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}
Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.
利用李群证明了具有李氏结构的流形在无穷远处的注入半径是正的。
{"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}
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 $N leq 6$.
{"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}
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.
{"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}
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.
{"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}
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 $G(d,1,n)$.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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