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Coxeter Graphs and Towers of Algebras

  • Book
  • © 1989

Overview

Authors:
  1. Frederick M. Goodman

    1. Department of Mathematics, University of Iowa, Iowa City, USA

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  2. Pierre Harpe

    1. Section de Mathématiques, Université de Genève, Genève 24, Switzerland

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  3. Vaughan F. R. Jones

    1. Department of Mathematics, University of California - Berkeley, Berkeley, USA
      Mathematical Sciences Research Institute, Berkeley, USA

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Part of the book series: Mathematical Sciences Research Institute Publications (MSRI, volume 14)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-x
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  2. Matrices over the natural numbers: Values of the norms, classification, and variations

    • Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones
    Pages 1-27

  3. Towers of multi-matrix algebras

    • Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones
    Pages 28-127

  4. Finite von Neumann Algebras with Finite Dimensional Centers

    • Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones
    Pages 128-181

  5. Commuting sqares, subfactors, and the derived tower

    • Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones
    Pages 182-231

  6. Back Matter

    Pages 232-288
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Keywords

About this book

A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the fundamental nature of the new link invariants has led to connections with invariant theory, statistical mechanics and quantum theory. In turn, the link invariants, the notion of a quantum group, and the quantum Yang-Baxter equation have had a great impact on the study of subfactors. Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.

Authors and Affiliations

  • Department of Mathematics, University of Iowa, Iowa City, USA

    Frederick M. Goodman

  • Section de Mathématiques, Université de Genève, Genève 24, Switzerland

    Pierre Harpe

  • Department of Mathematics, University of California - Berkeley, Berkeley, USA

    Vaughan F. R. Jones

  • Mathematical Sciences Research Institute, Berkeley, USA

    Vaughan F. R. Jones

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