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Slowly Increasing Cohomology for Discrete Metric Spaces with Polynomial Growth

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Chinese Annals of Mathematics,Series B 2012年第5期33卷 681-694页

作者： xiaoman chen Shuyun WEI School of Mathematical Sciences Fudan University Shanghai 200433 China. Department of Mathematics Soochow University Suzhou 215006 Jiangsu China.

The authors introduce a kind of slowly increasing cohomology HS＊（X） for a discrete metric space X with polynomial growth, and construct a character map from the slowly increasing cohomology HS＊（X） into HC＊ont （S（X））, the continuous cyclic cohomol- ogy of the smooth subalgebra S（X） of the uniform Roe algebra B＊（X）. As an application, it is shown that the fundamental cocycle, associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth, is slowly increasing.

关键词： Slowly increasing cohomology Polynomial growth Uniform Roe algebra

Thompson's Group and the Linear Group GL_∞(Z)

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Chinese Annals of Mathematics,Series B 2011年第6期32卷 863-884页

作者： Yan WU xiaoman chen College of Mathematics Physics and Information Engineering Jiaxing University Jiaxing 314033 Zhejiang China School of Mathematical Sciences Fudan University Shanghai 200433 China

The authors study the finite decomposition complexity of metric spaces of H, equipped with different metrics, where H is a subgroup of the linear group GL∞（E）. It is proved that there is an injective Lipschitz map φ：（F, ds） --＊（H,d）, where F is the Thompson＇s group, ds the word-metric of F with respect to the finite generating set S and d a metric of H. But it is not a proper map. Meanwhile, it is proved that φ（F, ds） → （H, dl） is not a Lipschitz map, where dl is another metric of H.

关键词： Finite decomposition complexity Thompson's group F Word-metric Lipschitz map Reduced tree diagram

THE K-THEORY AND THE CLASSIFICATION OF THE IRRATIONAL ROTATION GROUPOID C^(*)-ALGEBRAS

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Chinese Annals of Mathematics,Series B 1997年第2期18卷 257-264页

作者： YAN SHAOZONG chen xiaoman XU SHENGZHI Institute of Mathematics Fudan UniversityShanghsi 200433China

The authors determine the invariants of the irrational rotationC^(*)-algebras over theL-shaped domain in C^(2) by the maximal radical series.

关键词： K-group Maximal radical series C^(*)-algebra

The φ-Group for n Submodules Systems as a Generalization of the K-Theory

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Chinese Annals of Mathematics,Series B 2014年第1期35卷 101-114页

作者： Dong LI xiaoman chen Shengzhi XU School of Mathematical Sciences Fudan University

In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical *** theory is related to the classification theory for indecomposa... 详细信息

关键词： System of n subspaces System of n submodules Ф-Group K-Theory Indecomposable system

On the Equi-nuclearity of Roe Algebras of Metric Spaces

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Chinese Annals of Mathematics,Series B 2010年第4期31卷 519-528页

作者： xiaoman chen Benyin FU Qin WANG School of Mathematical Sciences Fudan University Shanghai 200433 China Department of Applied Mathematics Donghua University Shanghai 200051 China

The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊（X） is not nuclear.

关键词： Nuclear C^*-algebra Uniform Roe algebra Equi-nuclear uniform Roe algebra

Relative equivariant coarse index and relative L^(2)-index

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Science China Mathematics 2023年第7期66卷 1449-1472页

作者： xiaoman chen Yanlin Liu Dapeng Zhou School of Mathematical Sciences Fudan UniversityShanghai 200433China School of Statistics and Information Shanghai University of International Business and EconomicsShanghai 201620China Research Center for Operator Algebras East China Normal UniversityShanghai 200062China

In this paper,we define a relative equivariant coarse index for proper actions and a relative L^(2)-*** derive a relative equivariant coarse index theorem connecting the relative equivariant coarse index with the localized equivariant coarse ***,we present a calculation formula on the relative L^(2)-index and provide a relative L^(2)-index *** work is an expansion of the relative index theory which reflects the difference between two manifolds.

关键词： relative equivariant coarse index relative L^(2)-index regular cover Roe algebra

HANKEL OPERATORS AND HANKEL ALGEBRAS

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Chinese Annals of Mathematics,Series B 1998年第1期19卷 65-76页

作者： YAN SHAOZONG chen xiaoman GUO KUNYU Fudan Univ Inst Math Shanghai 200433 Peoples R China

The authors study the basic properties of Hankel operators and the structures of Hankel algebras relative to ordered groups,providing a new class of C*-algebras which are very useful in general C*-algebra theory.

关键词： Hankel operator Hankel algebra Commutator ideal

THE K-THEORY AND THE CLASSIFICATION OF THE IRRATIONAL ROTATION GROUPOID C-ALGEBRAS

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Chinese Annals of Mathematics,Series B 1997年第2期 120-127页

作者： YAN SHAOZONG * chen xiaoman * XU SHENGZHI *

ＴＨＥＫＴＨＥＯＲＹＡＮＤＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＴＨＥＩＲＲＡＴＩＯＮＡＬＲＯＴＡＴＩＯＮＧＲＯＵＰＯＩＤＣＡＬＧＥＢＲＡＳＹＡＮＳＨＡＯＺＯＮＧＣＨＥＮＸＩＡＯＭＡＮＸＵＳＨＥＮＧＺＨＩ... 详细信息

ＴＨＥＫＴＨＥＯＲＹＡＮＤＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＴＨＥＩＲＲＡＴＩＯＮＡＬＲＯＴＡＴＩＯＮＧＲＯＵＰＯＩＤＣＡＬＧＥＢＲＡＳＹＡＮＳＨＡＯＺＯＮＧＣＨＥＮＸＩＡＯＭＡＮＸＵＳＨＥＮＧＺＨＩＡｂｓｔｒａｃｔＴｈｅａｕｔｈｏｒ...

关键词：  group Maximal radical series C * algebra

IRRATIONAL ROTATION c-ALGEBRA FOR GROUPOID c-ALGEBRA

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Chinese Annals of Mathematics,Series B 1995年第4期16卷 445-452页

作者： chen xiaoman XU QINGXIANG XU SHENGZHI (Institute of Mathematics, F’udan University, Shanghai 200433, China.) FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

This paper characterizes the irrational rotaion C-algebra associated with the Toeplitz Calgebraover the L-shaped domain in in the sense of the maximal radical series, which is an isomorphism invariant.

关键词： L-shaped domain Toeplitz C-algebra Irrational rotation Invariant subset Maximal ideal.