Bratteli, Ola.
Representation theory and numerical AF-invariants : the representations and centralizers of certain states on Od / [electronic resource] Ola Bratteli, Palle E.T. Jorgensen, Vasyl� Ostrovs�ky�i. - Providence, R.I. : American Mathematical Society, 2004. - 1 online resource (xviii, 178 p. : ill.) - Memoirs of the American Mathematical Society, v. 797 0065-9266 (print); 1947-6221 (online); .
"March 2004, volume 168, number 797 (second of 4 numbers)."
Includes bibliographical references (p. 166-169).
A. Representation theory 1. General representations of $\mathcal _d$ on a separable Hilbert space 2. The free group on $d$ generators 3. $\beta $-KMS states for one-parameter subgroups of the action of $\mathbb ^d$ on $\mathcal _d$ 4. Subalgebras of $\mathcal _d$ B. Numerical AF-invariants 5. The dimension group of $\mathfrak _L$ 6. Invariants related to the Perron-Frobenius eigenvalue 7. The invariants $N$, $D$, Prim($m_N$), Prim($R_D$), Prim($Q_$) 8. The invariants $K_0 (\mathfrak _L) \otimes _} \mathbb _n$ and $(\operatorname \tau )\otimes _} \mathbb _n$ for $n = 2, 3, 4$, ... 9. Associated structure of the groups $K_0 (\mathfrak _L)$ and $\operatorname \tau $ 10. The invariant $\operatorname (\tau (K_0(\mathfrak _L)), \operatorname \tau )$ 11. Scaling and non-isomorphism 12. Subgroups of $G_0 = \bigcup ^\infty _ J^_0 \mathcal $ 13. Classification of the AF-algebras $\mathfrak _L$ with rank $(K_0 (\mathfrak _L)) = 2$ 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
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470403959 (online)
Ergodic theory.
Representations of groups.
Selfadjoint operators.
Linear operators.
QA3 QA611.5 / .A57 no. 797
510 s 515/.48
Representation theory and numerical AF-invariants : the representations and centralizers of certain states on Od / [electronic resource] Ola Bratteli, Palle E.T. Jorgensen, Vasyl� Ostrovs�ky�i. - Providence, R.I. : American Mathematical Society, 2004. - 1 online resource (xviii, 178 p. : ill.) - Memoirs of the American Mathematical Society, v. 797 0065-9266 (print); 1947-6221 (online); .
"March 2004, volume 168, number 797 (second of 4 numbers)."
Includes bibliographical references (p. 166-169).
A. Representation theory 1. General representations of $\mathcal _d$ on a separable Hilbert space 2. The free group on $d$ generators 3. $\beta $-KMS states for one-parameter subgroups of the action of $\mathbb ^d$ on $\mathcal _d$ 4. Subalgebras of $\mathcal _d$ B. Numerical AF-invariants 5. The dimension group of $\mathfrak _L$ 6. Invariants related to the Perron-Frobenius eigenvalue 7. The invariants $N$, $D$, Prim($m_N$), Prim($R_D$), Prim($Q_$) 8. The invariants $K_0 (\mathfrak _L) \otimes _} \mathbb _n$ and $(\operatorname \tau )\otimes _} \mathbb _n$ for $n = 2, 3, 4$, ... 9. Associated structure of the groups $K_0 (\mathfrak _L)$ and $\operatorname \tau $ 10. The invariant $\operatorname (\tau (K_0(\mathfrak _L)), \operatorname \tau )$ 11. Scaling and non-isomorphism 12. Subgroups of $G_0 = \bigcup ^\infty _ J^_0 \mathcal $ 13. Classification of the AF-algebras $\mathfrak _L$ with rank $(K_0 (\mathfrak _L)) = 2$ 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
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470403959 (online)
Ergodic theory.
Representations of groups.
Selfadjoint operators.
Linear operators.
QA3 QA611.5 / .A57 no. 797
510 s 515/.48