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murray–von neumann equivalence

Proceedings of the Edinburgh Mathematical Society (1)

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C*-ALGEBRAS THAT ARE ISOMORPHIC AFTER TENSORING AND FULL PROJECTIONS
Kazunori Kodaka
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 3 / October 2004

Published online by Cambridge University Press:

09 November 2004, pp. 659-668
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Let $A$ be a unital $C^*$-algebra and for each $n\in\mathbb{N}$ let $M_n$ be the $n\times n$ matrix algebra over $\mathbb{C}$. In this paper we shall give a necessary and sufficient condition that there is a unital $C^*$-algebra $B$ satisfying $A\not\cong B$ but for which $A\otimes M_n\cong B\otimes M_n$ for some $n\in\mathbb{N}\setminus\{1\}$. Also, we shall give some examples of unital $C^*$-algebras satisfying the above property.
AMS 2000 Mathematics subject classification: Primary 46L05