Representation Theory and Numerical AF-Invariants : The representations and centralizers of certain states on Od.

Intro -- Contents -- Abstract -- Preface -- Introduction -- Part A. Representation Theory -- Chapter 1. General representations of O[sub(d)] on a separable Hilbert space -- Chapter 2. The free group on d generators -- Chapter 3. 946-KMS states for one-parameter subgroups of the action of T[sub(d)] on O[sub(d)] -- Chapter 4. Subalgebras of O[sub(d)] -- Part B. Numerical AF-Invariants -- Chapter 5. The dimension group of u[sub(L)] -- Chapter 6. Invariants related to the Perron-Frobenius eigenvalue -- Chapter 7. The invariants N, D, Prim(m[sub(N)]), Prim(R[sub(D)]), Prim(Q[sub(N-D)]) -- Chapter 8. The invariants K[sub(0)] (u[sub(L)]) [sub(⊗z)]Z[sub(n)] and (ker T)[sub(⊗z)]Z[sub(n)] for n = 2, 3 , 4 , ... -- Chapter 9. Associated structure of the groups K[sub(0)] (u[sub(L)]) and kerT -- Chapter 10. The invariant Ext (T (K[sub(0)] (u[sub(L)]), ker T) -- Chapter 11. Scaling and non-isomorphism -- Chapter 12. Subgroups of G[sub(0)] = U[sup(∞)][sub(n=0)] J[sup(…n)][sub(0)]L -- Chapter 13. Classification of the AF-algebras u[sub(L)] with rank K[sub(0)] (u[sub(L)]) = 2 -- Chapter 14. Linear algebra of J -- Chapter 15. Lattice points -- Chapter 16. Complete classification in the cases λ= 2, N = 2, 3,4 -- Chapter 17. Complete classification in the case λ = m[sub(N)] -- 1. The case N = 1 -- 2. The case N = 2 -- 3. The case N = 3 -- 4. The case N ≤ 4 -- Chapter 18. Further comments on two examples from Chapter 16 -- Bibliography -- List of Figures -- List of Tables -- List of Terms and Symbols.

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