caa a22 4500 606161279 CHVBK 20210128100634.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9509-4 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9509-4 Kawamura Katsunori College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, 525-8577, Kusatsu, Shiga, Japan aut Classification of Sub-Cuntz States [Elektronische Daten] [Katsunori Kawamura] Let O n $\mathcal {O}_{n}$ denote the Cuntz algebra for 2 ≤ n < ∞ $2\leq n<\infty $ . With respect to a homogeneous embedding of O n m $\mathcal {O}_{n^{m}}$ into O n $\mathcal {O}_{n}$ , an extension of a Cuntz state on O n m $\mathcal {O}_{n^{m}}$ to O n $\mathcal {O}_{n}$ 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. Springer Science+Business Media Dordrecht, 2014 Extension of state nationallicence Sub-Cuntz state nationallicence Tensor product formula nationallicence Matricization nationallicence Free semigroup nationallicence Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 555-584 1386-923X 18:2<555 2015 18 10468 https://doi.org/10.1007/s10468-014-9509-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9509-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kawamura Katsunori College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, 525-8577, Kusatsu, Shiga, Japan aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 555-584 1386-923X 18:2<555 2015 18 10468