Some weakly inner automorphisms of the Cuntz algebras

Tsui, Sze-Kai

doi:10.1090/S0002-9939-1995-1239808-X

Some weakly inner automorphisms of the Cuntz algebras
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by Sze-Kai Tsui

Proc. Amer. Math. Soc. 123 (1995), 1719-1725

DOI: https://doi.org/10.1090/S0002-9939-1995-1239808-X

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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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