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arXiv · 1006.4791

The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms

Roberto Conti·Jeong Hee Hong·Wojciech Szymanski
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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.

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Roberto Conti, Jeong Hee Hong, Wojciech Szymanski. 2010-06-24. The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms. https://arxiv.org/abs/1006.4791

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