Morita equivalence and duality. by P. M. Cohn

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Published by Queen Mary College in London .

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SeriesMathematics notes
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Open LibraryOL20863474M
ISBN 100902480006

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Morita equivalence and duality (Queen Mary College mathematics notes) Unknown Binding – January 1, by P. M Cohn (Author) See all formats and editions Hide other formats and editions. Enter your mobile number or email address below and we'll send you a link to download the free Kindle App.

Author: P. M Cohn. Additional Physical Format: Online version: Cohn, P.M. (Paul Moritz). Morita equivalence and duality. London: Queen Mary College, [?] (OCoLC) COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Morita equivalence and duality Paperback – January 1, by P. M Cohn (Author) See all formats and editions Hide other formats and editions. Price New from Author: P. M Cohn. Morita-equivalence: a topos-theoretic perspective Olivia Caramello Introduction Toposes as bridges Dualities from topos-theoretic ‘bridges’ Topos-theoretic ‘bridges’ from dualities Dualities versus Morita-equivalences Some examples For further reading Topos à l’IHES Duality and Morita-equivalence In this lecture I shall approach the.

In this paper, we begin by reviewing the material necessary to define Morita equiva-lence, and we examine two classical examples of Morita equivalence. We then delve into what is now called “Morita theory”, which is in regards to the key theorems of Morita in [Mor58], the results leading up to them, and their immediate consequences.

to be Morita equivalent when their module categories are equivalent. In many cases, we often only care about rings up to Morita equivalence.

If this is the case, then given a ring A, we’d like to nd some particularly nice representative of the Morita equivalence class of A. 2 Morita Equivalence First some notation: Let R be a ring.

ELSEVIER Nuclear Physics B [PM] () B Morita equivalence and duality Albert Schwarz 1 Department of Mathematics, University of California, Davis, CAUSA Received 15 July ; accepted 3 August Abstract It was shown by Connes, Douglas, Schwarz [hep-th/] that one can compactify M(atrix) theory on a non-commutative torus To.

: Duality for modules and its applications in the theory of rings with minimum condition. Science reports of the Tokyo Kyoiku Daigaku, Section A, 6 (), Would someone know whether this is the right paper to look at, for Morita equivalence.

[1] K. Morita, Sci. Reports Tokyo Kyoiku Dajkagu A, 6 () pp. 83– [2] H. Bass, "Algebraic $K$-theory", Benjamin () [3] C. Faith, "Algebra: rings, modules.

In this chapter we introduce Morita duality. Roughly speaking, these theorems are dual to the Morita theorems on category equivalence (Chapter 12). Morita equivalence and T-duality (or Bversus Θ) B. Pioline∗ Centre de Physique Th´eorique†, Ecole Polytechnique, F Palaiseau, France A. Schwarz Institut des Hautes Etudes Scientifiques, Le Bois-Marie, F Bures-sur-Yvette, France Dept.

of Mathematics, University of California, Davis, CA USA. T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, I will show that the duality fits naturally into at least one framework for assessing equivalence.

T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM).

Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant abelian magnetic background. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We study the notion of Morita equivalence in various categories.

We start with Morita equivalence and Morita duality in pure algebra. Then we consider strong Morita equivalence for C*-algebras and Morita equivalence for W*-algebras.

Finally, we look at the corresponding notions for groupoids (with structure) and. It has been a while since I have looked at it but from memory "Morita Equivalence and Duality" by Cohn is quite a nice book and I think it contains several examples (I hope that I am remembering correctly).

The Morita-equivalence between MV-algebras and abelian ℓ-groups with strong unit Olivia Caramello∗ and Anna Carla Russo Ap Abstract We show that the theory of MV-algebras is Morita-equivalent to that of abelian ℓ-groups with strong unit. This generalizes the well-known equivalence between the categories of set-based models of.

This includes a detailed discussion of Morita equivalence of \(C^*\)-algebras, a review of the necessary sheaf cohomology, and an introduction to recent developments in the area.

The book is accessible to students who are beginning research in operator algebras after a. Morita Equivalence Eamon Quinlan Given a (not necessarily commutative) ring, you can form its category of right modules. Take this category and replace the names of all the modules with dots.

The resulting category is a bunch of dots with a bunch of arrows. The question is: what can you then say about the original ring from this category of. In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties.

It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in Author(s): Schwarz, Albert | Abstract: It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus.

We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a generalization of non-classical duality conjectured in [1] for two-dimensional tori. For UHF C*-algebras, any,-equivalence preserves the dimension of the underlying Hilbert space of a repre- sentation, since any representation is a direct sum of representations with under- lying, separable, infinite dimensional Hilbert spaces; and direct sums are preserved by.

CBBOOK-DVR CBColby Janu Char Count= 0 vi Contents Cotilting Bimodules 97 Cotilting via Tilting and Morita Duality Weak Morita Duality Finitistic Cotilting Modules and Bimodules U-torsionless Linear Compactness Examples and Questions A Adjoints and Category Equivalence   This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses.

the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective. This book provides a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years.

In particular, during the past dozen or so years many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and.

We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM).

Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant Abelian magnetic background.

Morita equivalence for W -algebras to non-selfadjoint dual operator algebras. Our theory contains all examples considered up to this point in the literature of Morita-like equivalence in a dual (weak topology) setting. 3 Morita equivalence of dual operator algebras Chapter 6.

Morita equaivalence 41 60; Morita equivalence functors 41 60; Induction and Morita equivalence 43 62; Alternative definitions of standard modules 46 65; Base change 47 66; Ringel duality and double centralizer properties 49 68; Chapter 7.

On formal characters of imaginary modules 53 72; Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.

Schur-Weyl duality for gl(V) x Schur-Weyl duality for GL(V) x Historical interlude: Hermann Weyl at the intersection Morita equivalence References for historical interludes Mathematical references Chapter 1 Introduction The goal of this book is to give a \holistic" introduction to rep.

Idea. Derived Morita equivalence is a generalization of Morita equivalence to the “derived” context (homotopy theory of dg-algebras).Just as two k k-algebras are Morita equivalent if and only if their categories of left modules are equivalent, the coarser equivalence relation of derived Morita equivalence holds whenever for two differential graded algebras their (bounded) derived.

Rings and Categories of Modules / Edition 2 available in Hardcover, Paperback. Add to Wishlist This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses.

the Jacobson radical, the hom and tensor Price: $ The algebra K(H) is Morita equivalent to C [12, Examples and ], and Morita equivalence is an equivalence relation [12, Proposition ], so A is Morita equivalent to C;let AYC be anA–C imprimitivity bimodule.

Since a Hilbert C-module YC is a Hilbert space and K(YC) is then the. title = "Morita duality and noncommutative Wilson loops in two dimensions", abstract = "We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori.

a characterization of duality. In addition we will flnd a good form for the inverse equivalences involved. This is a somewhat streamlined version of the brilliant work of Morita in which these characterizations were flrst presented. We begin by reviewing the notion of generating treated in Exercise Consider left R-modules RGand RM.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We consider a variant of the notion of Morita equivalence appropriate to weak * closed algebras of Hilbert space operators, which we call weak Morita equivalence.

Namely: suppose that A and B are strongly Morita equivalent operator algebras in the sense of the first author, Muhly, and Paulsen, with associated.

Equivalence and duality: adjoint functors-- categories equivalent to act - S Morita equivalence of monoids-- endomorphism monoids of generators-- on morita duality. (source: Nielsen Book Data) Summary A discussion of monoids, acts and categories with applications to wreath products and graphs.

In this text, the authors give a modern treatment of the classification of continuous-trace C*-algebras up to Morita equivalence.

This includes a detailed discussion of Morita equivalence of C*-algebras, a review of the necessary sheaf cohomology, and an introduction to recent developments in the area.

The book is accessible to students who are beginning research in operator algebras after a. A. Rivero writes: Okay, I have no idea what Morita equivalence is. I am trying to learn it, remember. Robert writes: There are two characterisations of Morita equivalence (at least that come to my mind immediately): A A and B B are Morita equivalent if they are equivalent after tensoring with the compact operators (in which are in some sense the N → ∞ N\to\infty limit of the N × N N\times.

I agree that Morita equivalence is a good analogy for duality in QFT, via the reason in #6. But it seems sufficiently different from the discussion of “abstract and concrete duality”.

Of course at the bottom of it you may argue that one is dealing with equivalences of categories, one way or other.A property P in the class of all rings is said to be Morita invariant if, whenever R has property P and S is Morita equivalent to R, then S has property P as well.

By the example above, it is clear that commutativity is not a Morita invariant property.

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