Coxeter Graphs and Towers of Algebras

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

   PDF

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.

• Dimension
• Factor
• Invariant
• Microsoft Access
• algebra
• equation
• finite group
• graphs
• group
• invariant theory
• mathematics
• matrices
• matrix
• mechanics
• polynomial

• 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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