## Tokyo Journal of Mathematics

### Automorphisms of Unital $C^*$-Algebras Which are Strongly Morita Equivalent to Irrational Rotation $C^*$-Algebras

Kazunori KODAKA

#### Abstract

Let $B$ be a unital $C^*$-algebra which is strongly Morita equivalent to an irrational rotation $C^*$-algebra. Then Rieffel showed that it is isomorphic to $A_\theta\otimes M_n$ where $A_\theta$ is an irrational rotation $C^*$-algebra and $M_n$ is the $n\times n$ matrix algebra over $C$. In the present paper we will show that for any automorphism $\alpha$ of $A_\theta\otimes M_n$ there are unitary elements $w\in A_\theta\otimes M_n$, $W\in M_n$ and an automorphism $\beta$ of $A_\theta$ such that $\alpha=\mathrm{Ad}(w)\circ(\beta\otimes\mathrm{Ad}(W))$.

#### Article information

Source
Tokyo J. Math., Volume 12, Number 1 (1989), 175-180.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270133556

Digital Object Identifier
doi:10.3836/tjm/1270133556

Mathematical Reviews number (MathSciNet)
MR1001740

Zentralblatt MATH identifier
0734.46039

#### Citation

KODAKA, Kazunori. Automorphisms of Unital $C^*$-Algebras Which are Strongly Morita Equivalent to Irrational Rotation $C^*$-Algebras. Tokyo J. Math. 12 (1989), no. 1, 175--180. doi:10.3836/tjm/1270133556. https://projecteuclid.org/euclid.tjm/1270133556