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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.
Coxeter Graphs and Towers of Algebras
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Other books in this series. Box Splines Carl de Boor.
Mathematical Sciences Research Institute Publications: Manifolds, Curves, and Surfaces Marcel Berger. Topology of Stratified Spaces Greg Friedman. Table of contents 1.
Matrices over the natural numbers: Proof of Kronecker’s theorem. Graphs with norms no larger than 2. The set E of norms of graphs and integral matrices.
Coxeter Graphs and Towers of Algebras : Frederick Goodman :
Towers of multi-matrix algebras. Inclusion matrix and Bratteli diagram for inclusions of multi-matrix algebras. The fundamental construction and towers for multi-matrix algebras.
Markov traces on pairs of multi-matrix algebras. An approach to the non-generic case. A digression on Hecke algebras. The complex Hecke algebra defined by GLn q and its Borel subgroup. The Hecke algebras Hq,n. Complex representations of the symmetric group. Irreducible representations of Hq,n for q? The relationship between A? Finite algebfas Neumann algebras with finite dimensional centers.
Factors defined by icc groups. A digression on the Peterson inner product. Index for subfactors of II1 factors. Inclusions of finite von Neumann algebras coceter finite dimensional centers. Markov traces on EndN Ma generalization of index. Commuting squares, subfactors, and the derived tower. Examples of irreducible pairs of factors of index less than 4, and a lemma of C.
The derived tower and the Coxeter invariant. Examples of derived towers. The An Coxeter graphs. Some toers of derived towers for index 4 subfactors.
The derived tower for R? Classification of Coxeter graphs with spectral radius just beyond the Kronecker range.
Computations of characteristic polynomials for ordinary graphs. Proofs of theorems I. Hecke groups and other subgroups of PSL 2,?