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CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES saito-kurokawa举的同余和中心旋量l值的分母
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-10-14 DOI: 10.1017/S0017089521000331
N. Dummigan
{"title":"CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES","authors":"N. Dummigan","doi":"10.1017/S0017089521000331","DOIUrl":"https://doi.org/10.1017/S0017089521000331","url":null,"abstract":"Abstract Following Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45462562","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: 1
Weak amenability of free products of hyperbolic and amenable groups 双曲和可服从群的自由积的弱可服从性
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-10-14 DOI: 10.1017/S0017089521000458
I. Vergara
{"title":"Weak amenability of free products of hyperbolic and amenable groups","authors":"I. Vergara","doi":"10.1017/S0017089521000458","DOIUrl":"https://doi.org/10.1017/S0017089521000458","url":null,"abstract":"Abstract We show that if G is an amenable group and H is a hyperbolic group, then the free product \u0000$Gast H$\u0000 is weakly amenable. A key ingredient in the proof is the fact that \u0000$Gast H$\u0000 is orbit equivalent to \u0000$mathbb{Z}ast H$\u0000 .","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44149633","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
Left regular representations of Garside categories I. C*-algebras and groupoids Garside范畴I. C*-代数与群拟的左正则表示
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-10-09 DOI: 10.1017/S0017089522000106
Xin Li
{"title":"Left regular representations of Garside categories I. C*-algebras and groupoids","authors":"Xin Li","doi":"10.1017/S0017089522000106","DOIUrl":"https://doi.org/10.1017/S0017089522000106","url":null,"abstract":"Abstract We initiate the study of C*-algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We develop a general classification result for closed invariant subspaces of our groupoids as well as criteria for topological freeness and local contractiveness, properties which are relevant for the structure of the corresponding C*-algebras. Our results provide a conceptual explanation for previous results on gauge-invariant ideals of higher rank graph C*-algebras. As another application, we give a complete analysis of the ideal structures of C*-algebras generated by left regular representations of Artin–Tits monoids.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47764107","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: 8
CORRIGENDUM TO: A FAST ALGORITHM FOR CALCULATING S-INVARIANTS 更正TO：一种计算S-不变量的快速算法
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-09-20 DOI: 10.1017/s001708952100032x
D. Schütz
{"title":"CORRIGENDUM TO: A FAST ALGORITHM FOR CALCULATING S-INVARIANTS","authors":"D. Schütz","doi":"10.1017/s001708952100032x","DOIUrl":"https://doi.org/10.1017/s001708952100032x","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45320381","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 boson-fermion correspondence in cohomological Donaldson–Thomas theory 同调Donaldson–Thomas理论中的玻色子-费米子对应关系
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-09-20 DOI: 10.1017/S001708952200009X
Ben Davison
{"title":"A boson-fermion correspondence in cohomological Donaldson–Thomas theory","authors":"Ben Davison","doi":"10.1017/S001708952200009X","DOIUrl":"https://doi.org/10.1017/S001708952200009X","url":null,"abstract":"Abstract We introduce and study a fermionisation procedure for the cohomological Hall algebra \u0000$mathcal{H}_{Pi_Q}$\u0000 of representations of a preprojective algebra, that selectively switches the cohomological parity of the BPS Lie algebra from even to odd. We do so by determining the cohomological Donaldson–Thomas invariants of central extensions of preprojective algebras studied in the work of Etingof and Rains, via deformed dimensional reduction. Via the same techniques, we determine the Borel–Moore homology of the stack of representations of the \u0000$unicode{x03BC}$\u0000 -deformed preprojective algebra introduced by Crawley–Boevey and Holland, for all dimension vectors. This provides a common generalisation of the results of Crawley-Boevey and Van den Bergh on the cohomology of smooth moduli schemes of representations of deformed preprojective algebras and my earlier results on the Borel–Moore homology of the stack of representations of the undeformed preprojective algebra.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44380003","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: 5
GMJ volume 63 issue 3 Cover and Front matter GMJ第63卷第3期封面和封面问题
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-09-01 DOI: 10.1017/s0017089521000252
{"title":"GMJ volume 63 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s0017089521000252","DOIUrl":"https://doi.org/10.1017/s0017089521000252","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43167139","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
GMJ volume 63 issue 3 Cover and Back matter GMJ第63卷第3期封面和封底
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-09-01 DOI: 10.1017/s0017089521000264
{"title":"GMJ volume 63 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0017089521000264","DOIUrl":"https://doi.org/10.1017/s0017089521000264","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42826493","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 computation of Hopf 2-cocycles with an example of diagonal type 关于Hopf-2-环的计算——以对角型为例
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-08-25 DOI: 10.1017/S0017089522000192
Agustín García Iglesias, José Ignacio Sánchez
{"title":"On the computation of Hopf 2-cocycles with an example of diagonal type","authors":"Agustín García Iglesias, José Ignacio Sánchez","doi":"10.1017/S0017089522000192","DOIUrl":"https://doi.org/10.1017/S0017089522000192","url":null,"abstract":"Abstract We present a framework for the computation of the Hopf 2-cocycles involved in the deformations of Nichols algebras over semisimple Hopf algebras. We write down a recurrence formula and investigate the extent of the connection with invariant Hochschild cohomology in terms of exponentials. As an example, we present detailed computations leading to the explicit description of the Hopf 2-cocycles involved in the deformations of a Nichols algebra of Cartan type \u0000$A_2$\u0000 with \u0000$q=-1$\u0000 , a.k.a. the positive part of the small quantum group \u0000$mathfrak{u}^+_{sqrt{-text{1}}}(mathfrak{sl}_3)$\u0000 . We show that these cocycles are generically pure, that is they are not cohomologous to exponentials of Hochschild 2-cocycles.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48111784","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
THE PROFINITE COMPLETION OF A PROFINITE PROJECTIVE GROUP 无限射影群的无限补全
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-08-23 DOI: 10.1017/S0017089521000240
Tamar Bar-On
{"title":"THE PROFINITE COMPLETION OF A PROFINITE PROJECTIVE GROUP","authors":"Tamar Bar-On","doi":"10.1017/S0017089521000240","DOIUrl":"https://doi.org/10.1017/S0017089521000240","url":null,"abstract":"Abstract We prove that the profinite completion of a profinite projective group is projective.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47915355","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: 2
Proper Lie automorphisms of incidence algebras 关联代数的真李自同构
IF 0.5 4区 数学
Glasgow Mathematical Journal Pub Date : 2021-08-09 DOI: 10.1017/S0017089522000015
É. Fornaroli, M. Khrypchenko, E. A. Santulo
{"title":"Proper Lie automorphisms of incidence algebras","authors":"É. Fornaroli, M. Khrypchenko, E. A. Santulo","doi":"10.1017/S0017089522000015","DOIUrl":"https://doi.org/10.1017/S0017089522000015","url":null,"abstract":"Abstract Let X be a finite connected poset and K a field. We study the question, when all Lie automorphisms of the incidence algebra I(X, K) are proper. Without any restriction on the length of X, we find only a sufficient condition involving certain equivalence relation on the set of maximal chains of X. For some classes of posets of length one, such as finite connected crownless posets (i.e., without weak crown subposets), crowns, and ordinal sums of two anti-chains, we give a complete answer.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42368348","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: 4
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