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## Über dieses Buch

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.

## Inhaltsverzeichnis

### Chapter 1. Matrices over the natural numbers: Values of the norms, classification, and variations

Abstract
As already mentioned, the initial problem for this chapter is combinatorial: it is the classification of finite matrices over the nonnegative integers = {0,1,2,····} which have Euclidean operator norms no larger than 2. The reader should be aware from the start that most matrices below are not square.
Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones

### Chapter 2. Towers of multi-matrix algebras

Abstract
The first purpose of this chapter is to study inclusions of one finite dimensional semi-simple algebra in another.
Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones

### Chapter 3. Finite von Neumann Algebras with Finite Dimensional Centers

Abstract
In this chapter we study pairs of finite von Neumann algebras with finite dimensional centers, and the index of such pairs.
Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones

### Chapter 4. Commuting sqares, subfactors, and the derived tower

Abstract
There are two main themes in this chapter. The first is the approximation of a pair N ⊂ M of hyperfinite II1 factors by pairs Cn ⊂ Bn of finite dimensional von Neumann algebras, with
$$\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {N \subset M} \\ { \cup \quad \cup } \\ \end{array} } \\ {\begin{array}{*{20}{c}} {{{C}_{{n + 1}}} \subset {{B}_{{n + {{1}^{.}}}}}} \\ { \cup \quad \cup } \\ \end{array} } \\ {{{C}_{n}} \subset {{B}_{n}}} \\ \end{array}$$
.
Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones

### Backmatter

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