On The Classification Of C Algebras Of Real Rank Zero Inductive Limits Of Matrix Algebras Over Non Hausdorff Graphs

Author : Hongbing Su
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 43,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826072

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On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs by Hongbing Su Pdf

This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.

Author : Hongbing Su
Publisher : National Library of Canada = Bibliothèque nationale du Canada
Page : 128 pages
File Size : 41,8 Mb
Release : 1992
Category : Electronic
ISBN : 0315787503

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On the Classification of C*-algebras of Real Rank Zero [microform] : Inductive Limits of Matrix Algebras Over Non-Hausdorff Graphs by Hongbing Su Pdf

Author : Liangqing Li
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 45,6 Mb
Release : 1997
Category : C*-algebras
ISBN : 9780821805961

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Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees by Liangqing Li Pdf

In this paper, it is shown that the simple unital C*-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over [italic capital]C([italic capital]X[subscript italic]i), where [italic capital]X[subscript italic]i are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of [italic capital]X[subscript italic]i = [0, 1]. The added generality is useful in the classification of more general inductive limit C*-algebras.

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 48,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804032

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Classification of Direct Limits of Even Cuntz-Circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy.

Author : Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 47,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401728232

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Quantum and Non-Commutative Analysis by Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima Pdf

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Author : Richard Herman,Betül Tanbay
Publisher : CRC Press
Page : 336 pages
File Size : 49,8 Mb
Release : 1993-11-15
Category : Mathematics
ISBN : 9781439863510

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Operator Algebras, Mathematical Physics, and Low Dimensional Topology by Richard Herman,Betül Tanbay Pdf

This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.

Author : Jack E. Graver,Mark E. Watkins
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 40,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805565

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Locally Finite, Planar, Edge-Transitive Graphs by Jack E. Graver,Mark E. Watkins Pdf

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.

Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 50,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803462

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Hilbert Modules over Operator Algebras by Paul S. Muhly,Baruch Solel Pdf

This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.

Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 40,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954

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Decision Problems for Equational Theories of Relation Algebras by H. Andréka,Steven R. Givant,I. Németi Pdf

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.

Author : Dieter Happel,Idun Reiten,Sverre O. Smalø
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 42,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804445

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Tilting in Abelian Categories and Quasitilted Algebras by Dieter Happel,Idun Reiten,Sverre O. Smalø Pdf

In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.

Author : Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 50,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805947

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Extended Affine Lie Algebras and Their Root Systems by Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao Pdf

This work is about extended affine Lie algebras (EALA's) and their root systems. EALA's were introduced by Hoegh-Krohn and Torresani under the name irreducible quasi-simple Lie algebras. The major objective is to develop enough theory to provide a firm foundation for further study of EALA's. The first chapter of the paper is devoted to establishing some basic structure theory. It includes a proof of the fact that, as conjectured by Kac, the invariant symmetric bilinear form on an EALA can be scaled so that its restriction to the real span of the root system is positive semi-definite. The second chapter studies extended affine root systems (EARS) which are an axiomatized version of the root systems arising from EALA's. The concept of a semilattice is used to give a complete description of EARS. In the final chapter, a number of new examples of extended affine Lie algebras are given. The concluding appendix contains an axiomatic characterization of the nonisotropic roots in an EARS in a more general context than the one used in the rest of the paper. Features: Provides a foundation for the study of an important class of Lie algebras that generalizes the class of affine Kac-Moody Lie algebras Includes material on Lie algebras and on root systems that can be read independently.

Author : Peter A. Fillmore and James A. Mingo
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 50,5 Mb
Release : 1998-07-28
Category : Operator algebras
ISBN : 0821871285

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Operator Algebras and Their Applications II by Peter A. Fillmore and James A. Mingo Pdf

The study of operator algebras, which grew out of von Neumann's work in the 1920s and 30s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality, with significant applications in other areas both within mathematics and in other fields. For this reason, and because of the existence of a strong Canadian school in the subject, the topic was a natural candidate for an emphasis year at The Fields Institute. This volume is the second selection of papers that arose from the seminars and workshops of a year-long program, Operator Algebras and Applications, that took place at The Fields Institute. Topics covered include the classification of amenable C*-algebras, lifting theorems for completely positive maps, and automorphisms of von Neumann algebras of type III.

Author : Edward Cline,Brian Parshall,Leonard Scott,Leonard L. Scott
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 46,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804889

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Stratifying Endomorphism Algebras by Edward Cline,Brian Parshall,Leonard Scott,Leonard L. Scott Pdf

Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \mathrm{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir presents a systematic study of the relationships between the representation theories of $R$ and $A$, especially those involving actual or potential structures on $A$ which ''stratify'' its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups. The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ''Specht/Weyl module'' correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.

Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 43,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.

Author : Ragnar-Olaf Buchweitz,John James Millson
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 48,9 Mb
Release : 1997
Category : CR submanifolds
ISBN : 9780821805411

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CR-Geometry and Deformations of Isolated Singularities by Ragnar-Olaf Buchweitz,John James Millson Pdf

In this power we show how to compute the parameter space [italic capital]X for the versal deformation of an isolated singularity ([italic capital]V, 0) under the assumptions [italic]dim [italic capital]V [greater than or equal to symbol] 4, depth {0} [italic capital]V [greater than or equal to symbol] 3, from the CR-structure on a link [italic capital]M of the singularity. We do this by showing that the space [italic capital]X is isomorphic to the space (denoted here by [script capital]K[subscript italic capital]M) associated to [italic capital]M by Kuranishi in 1977. In fact we produce isomorphisms of the associated complete local rings by producing quasi-isomorphisms of the controlling differential graded Lie algebras for the corresponding formal deformation theories.