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C*-ALGEBRAS THAT ARE ISOMORPHIC AFTER TENSORING AND FULL PROJECTIONS

Published online by Cambridge University Press:  09 November 2004

Kazunori Kodaka
Kazunori Kodaka
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa 903-0213, Japan (kodaka@math.u-ryukyu.ac.jp)
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Abstract

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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

Keywords

cancellationfull projectionMurray–von Neumann equivalencestrong Morita equivalencetensor product
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 3 , October 2004 , pp. 659 - 668
Copyright
Copyright © Edinburgh Mathematical Society 2004