Morita Equivalence and Its Generalizations
Author: Mingyi Wang
Publisher:
Published: 2001
Total Pages: 208
ISBN-13:
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Author: Mingyi Wang
Publisher:
Published: 2001
Total Pages: 208
ISBN-13:
DOWNLOAD EBOOKAuthor: David P. Blecher
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 109
ISBN-13: 082181916X
DOWNLOAD EBOOKWe employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and pairings (\cdot,\cdot) and [\cdot,\cdot] that induce (complete) isomorphisms betweenthe (balanced) Haagerup tensor products, X \otimes {hB} {} Y and Y \otimes {hA} {} X, and the algebras, A and B, respectively. Thus, formally, a Morita context is the same as that which appears in pure ring theory. The subtleties of the theory lie in the interplay between the pure algebra and the operator space geometry. Our analysis leads to viable notions of projective operator modules and dual operator modules. We show that two C*-algebras are Morita equivalent in our sense if and only ifthey are C*-algebraically strong Morita equivalent, and moreover the equivalence bimodules are the same. The distinctive features of the non-self-adjoint theory are illuminated through a number of examples drawn from complex analysis and the theory of incidence algebras over topological partial orders.Finally, an appendix provides links to the literature that developed since this Memoir was accepted for publication.
Author: Iain Raeburn
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 345
ISBN-13: 0821808605
DOWNLOAD EBOOKA modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR
Author: William Joseph Haboush
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 397
ISBN-13: 0821815407
DOWNLOAD EBOOKAuthor: William Joseph Haboush
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 429
ISBN-13: 0821815415
DOWNLOAD EBOOKProceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general
Author: Evan Elijah Washington
Publisher:
Published: 2018
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKDefinitional equivalence captures a sense in which theories are intertranslatable. Here I show that the same holds for a natural generalization of definitional equivalence to many-sorted theories: Morita equivalence. I show that Morita equivalence, a syntactic notion of equivalence of theories developed by Halvorson and Barrett, coincides with a generalized version of another syntactic notion created by Ahlbrandt and Ziegler (and more recently developed by Visser). This generalizes the earlier result of Halvorson and Barrett which showed that definitional equivalence and intertranslatability coincide in the case of single-sorted first-order theories. Definitional equivalence corresponds to being isomorphic in a category; Morita equivalence corresponds to being naturally isomorphic.
Author: Idun Reiten
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 216
ISBN-13: 9780821808504
DOWNLOAD EBOOKSurveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Henrique Bursztyn
Publisher:
Published: 2001
Total Pages: 196
ISBN-13:
DOWNLOAD EBOOKAuthor: Mati Kilp
Publisher: Walter de Gruyter
Published: 2011-06-24
Total Pages: 549
ISBN-13: 3110812908
DOWNLOAD EBOOKThe aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)