The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms
Operator Algebras
2012-08-16 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of O_n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift. If n is prime then this embedding is an isomorphism.
Keywords
Cite
@article{arxiv.1006.4791,
title = {The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms},
author = {Roberto Conti and Jeong Hee Hong and Wojciech Szymanski},
journal= {arXiv preprint arXiv:1006.4791},
year = {2012}
}