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Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d | | Ola Bratteli
; Palle E. T. Jorgensen
; Vasyl Ostrovskyi
; | | Date: |
6 Jul 1999 | | Journal: | Mem. Amer. Math. Soc. 168 (2004), no. 797 | | Subject: | Operator Algebras; Dynamical Systems; Functional Analysis; Representation Theory MSC-class: 46L30, 46L55, 46L89, 47A13, 47A67 (Primary) 47A20, 47D25, 43A65 (Secondary) | math.OA math.DS math.FA math.RT | | Affiliation: | University of Oslo), Palle E. T. Jorgensen (University of Iowa), Vasyl Ostrovskyi (National Academy of Sciences of Ukraine | | Abstract: | 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_alpha S_alpha^* =S_{alpha_{1}}...S_{alpha_{k}}S_{alpha_{k}}^*...S_{alpha_{1}}^* where alpha=(alpha_1...alpha_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_alpha S_alpha^*) =(S_{ialpha}S_{ialpha}^*)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. | | Source: | arXiv, math.OA/9907036 | | Services: | Forum | Review | PDF | Favorites | |
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