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Representation theory and numerical AF-invariants: the representations and centralizers of certain states on Od
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Representation theory and numerical AF-invariants: the representations and centralizers of certain states on Od

Ola Bratteli, Palle E T Jorgensen and Vasylʹ Ostrovsʹkyĭ
Memoirs of the American Mathematical Society, no. 797, American Mathematical Society
2004
DOI: 10.1090/memo/0797
url
https://doi.org/10.1090/memo/0797View
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Abstract

Let Od be the Cuntz algebra on generators Si,... , S^, 2 < d < oo. Let Vd C (9d be the abelian subalgebra generated by monomials SaS^ = Sai • • • SakS^k • • • *S*X where a = (ai.. . a^) ranges over all multi-indices formed from {1,... , d}. In any representation of Od-, Vd may be simultaneously diagonalized. Using Si (SaS^) = (Sialic*) ^ w e sno w that the operators Si from a general representation of Od may be expressed directly in terms of the spectral representation of T>d- We use this in describing a class of type III representations of Od and corresponding endomorphisms, and the heart of the memoir 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.
 Ergodic theory Selfadjoint operators Representations of groups Linear operators

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