Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d
| dc.creator | Bratteli, Ola | |
| dc.creator | Jorgensen, Palle E. T. | |
| dc.creator | Ostrovskyi, Vasyl | |
| dc.date | 1999-07-06 | |
| dc.date | 2003-05-27 | |
| dc.date.accessioned | 2026-07-07T05:29:48Z | |
| dc.date.available | 2026-07-07T05:29:48Z | |
| dc.description | Let O_d be the Cuntz algebra on generators S_1,...,S_d, 2 \leq d < \infty, and let D_d \subset O_d be the abelian subalgebra generated by monomials S_αS_α^* =S_{α_{1}}...S_{α_{k}}S_{α_{k}}^*...S_{α_{1}}^* where α=(α_1...α_k) ranges over all multi-indices formed from {1,...,d}. In any representation of O_d, D_d may be simultaneously diagonalized. Using S_i(S_αS_α^*) =(S_{iα}S_{iα}^*)S_i, we show that the operators S_i from a general representation of O_d may be expressed directly in terms of the spectral representation of D_d. We use this in describing a class of type III representations of O_d and corresponding endomorphisms, and the heart of the paper is a description of an associated family of AF-algebras arising as the fixed-point algebras of the associated modular automorphism groups. Chapters 5--18 are devoted to finding effective methods to decide isomorphism and non-isomorphism in this class of AF-algebras. | |
| dc.description | xiv+178 pages, AMS-LaTeX, wncyr font; changes in versions 2 and 3 only in Introduction, except minor typos; more sources in Bibliography (+17 in v2, +3 in v3); accepted for publication in Mem. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/9907036 | |
| dc.identifier | http://arxiv.org/abs/math/9907036 | |
| dc.identifier | Mem. Amer. Math. Soc. 168 (2004), no. 797 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78783 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | Functional Analysis | |
| dc.subject | Representation Theory | |
| dc.subject | 46L30, 46L55, 46L89, 47A13, 47A67 (Primary) 47A20, 47D25, 43A65 (Secondary) | |
| dc.title | Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d | |
| dc.type | text |