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- W2950872377 abstract "Let ${cal O}_n$ denote the Cuntz algebra for $2leq n<infty$. With respect to a homogeneous embedding of ${cal O}_{n^m}$ into ${cal O}_n$, an extension of a Cuntz state on ${cal O}_{n^m}$ to ${cal O}_n$ is called a sub-Cuntz state, which was introduced by Bratteli and Jorgensen. We show (i) a necessary and sufficient condition of the uniqueness of the extension, (ii) the complete classification of pure sub-Cuntz states up to unitary equivalence of their GNS representations, and (iii) the decomposition formula of a mixing sub-Cuntz state into a convex hull of pure sub-Cuntz states. Invariants of GNS representations of pure sub-Cuntz states are realized as conjugacy classes of nonperiodic homogeneous unit vectors in a tensor-power vector space. It is shown that this state parameterization satisfies both the $U(n)$-covariance and the compatibility with a certain tensor product. For proofs of main theorems, matricizations of state parameters and properties of free semigroups are used." @default.
- W2950872377 created "2019-06-27" @default.
- W2950872377 creator A5007465802 @default.
- W2950872377 date "2014-08-06" @default.
- W2950872377 modified "2023-09-24" @default.
- W2950872377 title "Classification of sub-Cuntz states" @default.
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- W2950872377 doi "https://doi.org/10.48550/arxiv.1408.1178" @default.
- W2950872377 hasPublicationYear "2014" @default.
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