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Monday, August 3, 2020 | History

2 edition of Morita equivalence and duality found in the catalog.

Morita equivalence and duality

P. M. Cohn

Morita equivalence and duality

by P. M. Cohn

  • 313 Want to read
  • 3 Currently reading

Published by Dillon"s Q.M.C. Bookshop in London .
Written in English

    Subjects:
  • Categories (Mathematics),
  • Modules (Algebra),
  • Rings (Algebra),
  • Duality theory (Mathematics)

  • Edition Notes

    Bibliography: p. [79]

    Statement[by] P. M. Cohn.
    SeriesQueen Mary College. Mathematics notes, Queen Mary College mathematical notes.
    Classifications
    LC ClassificationsQA169 .C58
    The Physical Object
    Pagination[3], 79 p.
    Number of Pages79
    ID Numbers
    Open LibraryOL5671392M
    LC Control Number68131114

      One which would take up Morita equivalence as an aspect of a 3-groupoid, as well as Lurie’s claim “The notion of Morita equivalence is most naturally formulated in the language of classifying ∞-topoi” (DAG V). I see there are also suggestions of Morita equivalence accounting for some string dualities, such as here. 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 .

    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. 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.

    Se-Jin Kim (). Strong Morita Equivalence and Imprimitivity Theorems. UWSpace. 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.


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Morita equivalence and duality by P. M. Cohn Download PDF EPUB FB2

Morita equivalence and duality (Queen Mary College mathematics notes) Unknown Binding – January 1, by P. M Cohn (Author)Author: P.

M Cohn. 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 by: 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 Toposes as bridges • The existence ofdifferent theorieswith the same classifying.

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. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.

Send article to Kindle To send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and. 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 In this chapter we introduce Morita duality. Roughly speaking, these theorems are dual to the Morita theorems on category equivalence (Chapter 12).

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 by: Japanese mathematician Kiiti Morita is known for having stated and proved a theorem which gave an equivalent condition for this equivalence in an influential paper, [Mor58].

This theorem plays an important role in modern algebra, and in his honour, this equivalence of module categories between two rings has been dubbed “Morita.

BMRS08 discusses an axiomatic definition of topological T-duality generalizing and refining T-duality between noncommutative spaces in terms of Morita equivalence to a special type of KK-equivalence, which defines a T-duality action that is of order two up to Morita equivalence.

Alongside with Morita equivalence one considers Morita duality, relating some subcategories of the categories of left $R$-modules and right $S$-modules (mostly the subcategories of finitely-generated modules). However, the very existence of such a duality places definite restrictions on. Abstract: 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. Additional Physical Format: Online version: Cohn, P.M. (Paul Moritz). Morita equivalence and duality.

London: Queen Mary College, [?] (OCoLC) The article concludes with a brief discussion of the relationship between equivalence and duality. Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of. Morita equivalence and moduli problems. Ask Question Asked 10 years, 4 months ago.

the module varieties of Morita-equivalent algebras are related via associated fibre bundle constructions. 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. Morita equivalence and duality Paperback – January 1, by P.

M Cohn (Author) See all formats and editions Hide other formats and editionsAuthor: P. M Cohn. 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.

JOURNAL OF PURE AND APPLIED ALGEBRA ELSEV Journal of Pure and Applied Algebra () Characterizations of injective cogenerators and Morita duality via equivalences and dualities Weimin Xue Department of Mathematics, Fujian Normal University, Fwhou, FujianPeople's Republic of China Communicated by A.

Blass; received 8 March Abstract We characterize. 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.

In this paper, we reanalyze and clarify the. 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. 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.Equivalence and duality for module categories: with tilting and cotilting for rings Robert R. Colby, Kent R. Fuller 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.We characterize Morita equivalence of theories in the sense of Johnstone in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson for cartesian, regular, coherent, geometric and first-order theories.