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QUELQUES TENTATIVES DE DÉFINIR UNE NOTION GÉNÉRALE DE GROUPES ET DE CORPS DE DIMENSION UN ET DE DÉTERMINER LEURS PROPRIÉTÉS ALGÉBRIQUES 一些尝试定义一维群和域的一般概念，并确定它们的代数性质
Confluentes Mathematici Pub Date : 2009-05-01 DOI: 10.1142/S1793744209000043
B. Poizat
{"title":"QUELQUES TENTATIVES DE DÉFINIR UNE NOTION GÉNÉRALE DE GROUPES ET DE CORPS DE DIMENSION UN ET DE DÉTERMINER LEURS PROPRIÉTÉS ALGÉBRIQUES","authors":"B. Poizat","doi":"10.1142/S1793744209000043","DOIUrl":"https://doi.org/10.1142/S1793744209000043","url":null,"abstract":"We make some attempts to define a general notion of groups and fields of dimension one, and to determine their algebraic properties.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"113 1","pages":"111-122"},"PeriodicalIF":0.0,"publicationDate":"2009-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74824486","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: 8
POLYNOMIAL DYNAMIC AND LATTICE ORBITS IN S-ARITHMETIC HOMOGENEOUS SPACES s算术齐次空间中的多项式动态轨道和点阵轨道
Confluentes Mathematici Pub Date : 2009-02-11 DOI: 10.1142/S1793744210000120
A. Guilloux
{"title":"POLYNOMIAL DYNAMIC AND LATTICE ORBITS IN S-ARITHMETIC HOMOGENEOUS SPACES","authors":"A. Guilloux","doi":"10.1142/S1793744210000120","DOIUrl":"https://doi.org/10.1142/S1793744210000120","url":null,"abstract":"Consider a homogeneous space under a locally compact group G and a lattice Γ in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder how to describe its repartition. One then adopts a dynamical point of view and compare the asymptotic distribution of points in the orbits with the natural measure on the space. In the setting of Lie groups and their homogeneous spaces, several results show an equidistribution of points in the orbits. We address here this problem in the setting of p-adic and S-arithmetic groups.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"6 1","pages":"1-35"},"PeriodicalIF":0.0,"publicationDate":"2009-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87053443","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: 5
RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES 作为度量结构的模型随机化
Confluentes Mathematici Pub Date : 2009-01-11 DOI: 10.1142/S1793744209000080
I. Yaacov, H. Keisler
{"title":"RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES","authors":"I. Yaacov, H. Keisler","doi":"10.1142/S1793744209000080","DOIUrl":"https://doi.org/10.1142/S1793744209000080","url":null,"abstract":"The notion of a randomization of a rst order structure was introduced by Keisler in the paper Randomizations of Models, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original rst order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete rst order theory is a complete theory in continuous logic that admits elimination of quantiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"8 1","pages":"197-223"},"PeriodicalIF":0.0,"publicationDate":"2009-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84459948","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: 43
THE POINCARÉ ALGEBRA IN THE CONTEXT OF AGEING SYSTEMS: LIE STRUCTURE, REPRESENTATIONS, APPELL SYSTEMS AND COHERENT STATES 老化系统背景下的poincarÉ代数:谎言结构，表示，上诉系统和连贯状态
Confluentes Mathematici Pub Date : 2006-01-12 DOI: 10.1142/S1793744212500065
M. Henkel, R. Schott, S. Stoimenov, J. Unterberger
{"title":"THE POINCARÉ ALGEBRA IN THE CONTEXT OF AGEING SYSTEMS: LIE STRUCTURE, REPRESENTATIONS, APPELL SYSTEMS AND COHERENT STATES","authors":"M. Henkel, R. Schott, S. Stoimenov, J. Unterberger","doi":"10.1142/S1793744212500065","DOIUrl":"https://doi.org/10.1142/S1793744212500065","url":null,"abstract":"By introducing an unconventional realization of the Poincare algebra of special relativity as conformal transformations, we show how it may occur as a dynamical symmetry algebra for ageing systems in non-equilibrium statistical physics and give some applications, such as the computation of two-time correlators. We also discuss infinite-dimensional extensions of in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz function for as a tool for bosonic quantization.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"258 1","pages":"1250006"},"PeriodicalIF":0.0,"publicationDate":"2006-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77091742","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: 40
A FORMALISM FOR THE RENORMALIZATION PROCEDURE 重整化过程的形式主义
Confluentes Mathematici Pub Date : 2003-12-10 DOI: 10.1142/S1793744212400026
D. Tamarkin
{"title":"A FORMALISM FOR THE RENORMALIZATION PROCEDURE","authors":"D. Tamarkin","doi":"10.1142/S1793744212400026","DOIUrl":"https://doi.org/10.1142/S1793744212400026","url":null,"abstract":"We describe a formalism underlying the renormalization procedure and Batalin-Vilkoviski formalism. In the framework of this formalism, we give a mathematical definition of OPE-algebra and describe an additional natural structure which produces a *-Lie algebra structure on the (cohomologically shifted) D-module of observables, whence an $L_infty$ algebra structure on the space of global sections of the de Rham complex of this D-module. Given a Maurer-Cartan element in this $L_infty$ algebra, we construct a deformation of the OPE-algebra, which is exactly the desired renormalization.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"14 1","pages":"1240002"},"PeriodicalIF":0.0,"publicationDate":"2003-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75744203","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: 4
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