Cargando…
Representation theory and numerical AF-invariants : the representations and centralizers of certain states on Od /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
2004.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 797. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- A. Representation theory 1. General representations of $\mathcal {O}_d$ on a separable Hilbert space 2. The free group on $d$ generators 3. $\beta $-KMS states for one-parameter subgroups of the action of $\mathbb {T}^d$ on $\mathcal {O}_d$ 4. Subalgebras of $\mathcal {O}_d$ B. Numerical AF-invariants 5. The dimension group of $\mathfrak {A}_L$ 6. Invariants related to the Perron-Frobenius eigenvalue 7. The invariants $N$, $D$, Prim($m_N$), Prim($R_D$), Prim($Q_{N-D}$) 8. The invariants $K_0 (\mathfrak {A}_L) \otimes _{\mathbb {Z}} \mathbb {Z}_n$ and $(\operatorname {ker} \tau)\otimes _{\mathbb {Z}} \mathbb {Z}_n$ for $n = 2, 3, 4$ ... 9. Associated structure of the groups $K_0 (\mathfrak {A}_L)$ and $\operatorname {ker} \tau $ 10. The invariant $\operatorname {Ext}(\tau (K_0(\mathfrak {A}_L)), \operatorname {ker} \tau)$ 11. Scaling and non-isomorphism 12. Subgroups of $G_0 = \bigcup ^\infty _{n=0} J^{-n}_0 \mathcal {L}$ 13. Classification of the AF-algebras $\mathfrak {A}_L$ with rank $(K_0 (\mathfrak {A}_L)) = 2$ 14. Linear algebra of $J$ 15. Lattice points 16. Complete classification in the cases $\lambda = 2$, $N = 2, 3, 4$ 17. Complete classification in the case $\lambda = m_N$ 18. Further comments on two examples from Chapter 16.