Contents
Abstract vii
Preface ix
Introduction xi
Part A. Representation Theory 1
Chapter 1. General representations of Od on a separable Hilbert space 3
Chapter 2. The free group on d generators 12
Chapter 3. /3-KMS states for one-parameter subgroups
of the action of
Td
on Od 18
Chapter 4. Subalgebras of Od 22
Part B. Numerical AF-Invariants 43
Chapter 5. The dimension group of 21^ 45
Chapter 6. Invariants related to the Perron-Frobenius eigenvalue 58
Chapter 7. The invariants A/", D, Prim(rajv), Prim (/?£), Prim(Qjv_^) 61
Chapter 8. The invariants KQ (21L) ^ Z ^n and (ker r) 0z Z
n
for n = 2, 3,4,... 74
Chapter 9. Associated structure of the groups K$ (21L) and kerr 80
Chapter 10. The invariant Ext (r (K0 (2lL)), ker r) 85
Chapter 11. Scaling and non-isomorphism 90
Chapter 12. Subgroups of G0 = \J™=0 J^nC 113
Chapter 13. Classification of the AF-algebras
21L
with rank (AT0
(21L))
2 116
Chapter 14. Linear algebra of J 126
Chapter 15. Lattice points 129
Chapter 16. Complete classification in the cases A = 2, N = 2, 3,4 131
Chapter 17. Complete classification in the case A = rajv 141
1. The case N = 1 149
Previous Page Next Page