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

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

2010-03-09

arxiv.org/abs/1003.1815v1

J. Aust. Math. Soc. 89, 309-315 (2010)

Mathematics

Operator Algebras

Scientific paper

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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