Author | Goodman, Frederick M. author |
---|---|
Title | Coxeter Graphs and Towers of Algebras [electronic resource] / by Frederick M. Goodman, Pierre de la Harpe, Vaughan F. R. Jones |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9641-3 |
Descript | X, 288 p. online resource |
1. Matrices over the natural numbers: values of the norm, classification, and variations -- 1.1. Introduction -- 1.2. Proof of Kroneckerโs theorem -- 1.3. Decomposability and pseudo-equivalence -- 1.4. Graphs with norms no larger than 2 -- 1.5. The set E of norms of graphs and integral matrices -- 2. Towers of multi-matrix algebras -- 2.1. Introduction -- 2.2. Commutant and bicommutant -- 2.3. Inclusion matrix and Bratteli diagram for inclusions of multi-matrix algebras -- 2.4. The fundamental construction and towers for multi-matrix algebras -- 2.5. Traces -- 2.6. Conditional expectations -- 2.7. Markov traces on pairs of multi-matrix algebras -- 2.8. The algebras A?,k for generic ? -- 2.9. An approach to the non-generic case -- 2.10. A digression on Hecke algebras -- 2.11. The relationship between A?,n and the Hecke algebras -- 3. Finite von Neumann algebras with finite dimensional centers -- 3.1. Introduction -- 3.2. The coupling constant: definition -- 3.3. The coupling constant: examples -- 3.4. Index for subfactors of II1 factors -- 3.5. Inclusions of finite von Neumann algebras with finite dimensional centers -- 3.6. The fundamental construction -- 3.7. Markov traces on EndN(M), a generalization of index -- 4. Commuting squares, subfactors, and the derived tower -- 4.1. Introduction -- 4.2. Commuting squares -- 4.3. Wenzlโs index formula -- 4.4. Examples of irreducible pairs of factors of index less than 4, and a lemma of C. Skau -- 4.5. More examples of irreducible paris of factors, and the index value 3 + 31/2 -- 4.6. The derived tower and the Coxeter invariant -- 4.7. Examples of derived towers -- Appendix I. Classification of Coxeter graphs with spectral radius just beyond the Kronecker range -- I.1. The results -- I.2. Computations of characteristic polynomials for ordinary graphs -- I.3. Proofs of theorems I.1.2 and I.1.3 -- Appendix II.a. Complex semisimple algebras and finite dimensional C*-algebras -- Appendix III. Hecke groups and other subgroups of PSL(2,?) generated by parabolic pairs -- References