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Some weakly inner automorphisms of the Cuntz algebras

Author: Sze-Kai Tsui
Journal: Proc. Amer. Math. Soc. 123 (1995), 1719-1725
MSC: Primary 46L40; Secondary 46L05
MathSciNet review: 1239808
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Abstract: Let V be an $ n \times n$ unitary matrix. Then V induces an automorphism $ {O_V}$ of $ {O_\infty }$ and $ {O_n}$. It is shown in this paper that $ {O_V}$ is weakly inner. Let $ {F_n}$ be the UHF $ {C^ \ast }$-subalgebra of $ {O_n}$ and U be a unitary operator in the diagonal maximal abelian $ \ast $-subalgebra of $ {F_n}$. Then the automorphism $ {\lambda _U}$ of On defined by $ {\lambda _U}({S_i}) = {U^ \ast }{S_i}$, for each generator $ {S_i}$ of $ {O_n}$, is weakly inner. Any automorphism conjugate to either one mentioned above is also weakly inner.

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Keywords: Cuntz algebras, weakly inner automorphisms, FOCK representation, separable simple $ {C^ \ast }$ algebras, universally weakly inner automorphisms, outer automorphisms, permutations
Article copyright: © Copyright 1995 American Mathematical Society