C*-algebra Extensions and K-homology PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download C*-algebra Extensions and K-homology PDF full book. Access full book title C*-algebra Extensions and K-homology by Ronald G. Douglas. Download full books in PDF and EPUB format.
Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 9780691082660
Category : Mathematics
Languages : en
Pages : 112
Get Book Here
Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 9780691082660
Category : Mathematics
Languages : en
Pages : 112
Get Book Here
Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author: Huaxin Lin
Publisher: American Mathematical Soc.
ISBN: 0821826115
Category : Mathematics
Languages : en
Pages : 102
Get Book Here
Book Description
We show that the Weyl-von Neumann theorem for unitaries holds for [lowercase Greek]Sigma-unital [italic capital]A[italic capital]F-algebras and their multiplier algebras.
Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 1400881463
Category : Mathematics
Languages : en
Pages : 96
Get Book Here
Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author: Ronald G. Douglas
Publisher: Books on Demand
ISBN: 9780608066172
Category :
Languages : en
Pages : 93
Get Book Here
Book Description
Author: Ronald G. Douglas
Publisher: Books on Demand
ISBN: 9780608066172
Category : Algebra, Homological
Languages : en
Pages : 93
Get Book Here
Book Description
Author: Huaxin Lin
Publisher:
ISBN:
Category :
Languages : it
Pages : 89
Get Book Here
Book Description
Author: James Michael Gardner Fell
Publisher: American Mathematical Soc.
ISBN: 0821812904
Category : Banach algebras
Languages : en
Pages : 172
Get Book Here
Book Description
The main object of the present memoir is to show that the methods and results of Mackey (1958) and Blattner (1963) on the group extension representation problem go through without any essential change in the larger context of homogeneous Banach *-algebraic bundles (with enough cross sections). In order to dispense with separability we shall follow the topological methods of Blattner rather than Mackey's more detailed measure-theoretic analysis. Except for the last section, Part II of this memoir is in fact a rewriting of much of Blattner's papers (1963), making the modifications necessary in the larger context of bundles. The last Section 17 gives an account of the 'Mackey obstruction' in the nonseparable case, leading to an analogue (Theorem 17.2) of Theorem 8.2 of Mackey's paper for homogeneous Banach *-algebraic bundles, without separability restrictions. This is the culminating point of the present memoir.
Author: Jean-Claude Raoult
Publisher: Springer Science & Business Media
ISBN: 9783540552512
Category : Computers
Languages : en
Pages : 376
Get Book Here
Book Description
This volume contains selected papers presented at the seventeenth Colloquiumon Trees in Algebra and Programming (CAAP) held jointly with the European Symposium on Programming (ESOP) in Rennes, France, February 26-28, 1992 (the proceedings of ESOP appear in LNCS 582). The previous colloquia were held in France, Italy, Germany, Spain, Denmark and England. Every even year, as in 1992, CAAP is held jointly with ESOP; every other year, it is part of TAPSOFT (Theory And Practice of SOFTware development). In the beginning, CAAP was devoted to algebraic and combinatorial properties of trees and their role in various fields of computer science. The scope of CAAP has now been extended to other discrete structures, like graphs, equations and transformations of graphs, and their links with logical theories. The programme committee received 40 submissions, from which 19 papers have been selected for inclusion inthis volume.
Author: W Felscher
Publisher: CRC Press
ISBN: 9789056992668
Category : Mathematics
Languages : en
Pages : 298
Get Book Here
Book Description
This is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Löwenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations of elementary classes with the help of ultraproducts. Logic is based exclusively on semantics: truth and satisfiability of formulas in structures are the basic notions. The methods are algebraic in the sense that notions such as homomorphisms and congruence relations are applied throughout in order to gain new insights. These concepts are developed and can be viewed as a first course on universal algebra. The approach to algorithms generating semantical consequences is algebraic as well: for equations in algebras, for propositional formulas, for open formulas of predicate logic, and for the formulas of quantifier logic. The structural description of logical consequence is a straightforward extension of that of equational consequence, as long as Boolean valued propositions and Boolean valued structures are considered; the reduction of the classical 2-valued case then depends on the Boolean prime ideal theorem.
Author: Klaus Thomsen
Publisher: American Mathematical Soc.
ISBN: 0821846922
Category : Mathematics
Languages : en
Pages : 138
Get Book Here
Book Description
The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.
