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Algebraic structures determined by 3 by 3 matrix geometry

Author: Martin E. Walter
Journal: Proc. Amer. Math. Soc. 131 (2003), 2129-2131
MSC (2000): Primary 46L89, 43A35; Secondary 43A40, 43A30
Published electronically: December 30, 2002
MathSciNet review: 1963763
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Abstract: Using a ``3 by 3 matrix trick'' we show that multiplication (an algebraic structure) in a $C$*-algebra ${\mathcal{A}}$ is determined by the geometry of the $C$*-algebra of the 3 by 3 matrices with entries from ${\mathcal{A}}$, $M_{3} ({\mathcal{A}})$. This is an example of an algebra-geometry duality which, we claim, has applications.

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Additional Information

Martin E. Walter
Affiliation: Department of Mathematics, Campus Box 395, University of Colorado, Boulder, Colorado 80309

Keywords: $C^{\ast }$-algebra, convolution, completely bounded, duality, Fourier-Stieltjes algebra, locally compact group, positive definite function, matrix entry, unitary representation
Received by editor(s): July 15, 2001
Received by editor(s) in revised form: February 10, 2002
Published electronically: December 30, 2002
Dedicated: Dedicated to Masamichi and Kyoko Takesaki and the memory of Yuki
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society