# Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d

@inproceedings{Bratteli1999RepresentationTA,
title={Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d},
author={Ola Bratteli and Palle E. T. Jorgensen and Vasyl Ostrovskyi},
year={1999}
}
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_{i\alpha}S_{i\alpha}^*)S_i, we show that the operators S_i from a… CONTINUE READING

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