Representation theory and numerical AF-invariants : [electronic resource] the representations and centralizers of certain states on Od / Ola Bratteli, Palle E.T. Jorgensen, Vasyl� Ostrovs�ky�i.

"March 2004, volume 168, number 797 (second of 4 numbers)."

Includes bibliographical references (p. 166-169).

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

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