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arXiv · 1003.1815

Automorphisms of the UHF algebra that do not extend to the Cuntz algebra

Roberto Conti
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Abstract

Automorphisms of the canonical core UHF-subalgebra F_n of the Cuntz algebra O_n do not necessarily extend to automorphisms of O_n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the matrix algebras M_n. In that case, necessary and sufficient conditions for the extension property are presented. It is also addressed the problem of extending to O_n the automorphisms of the diagonal D_n, which is a regular MASA with Cantor spectrum. In particular, it is shown the existence of product-type automorphisms of D_n that are not extensible to (possibly proper) endomorphisms of O_n.

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Roberto Conti. 2010-03-09. Automorphisms of the UHF algebra that do not extend to the Cuntz algebra. https://arxiv.org/abs/1003.1815

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