Algebraic structures determined by 3 by 3 matrix geometry

Walter, Martin

doi:10.1090/S0002-9939-02-06849-1

Algebraic structures determined by 3 by 3 matrix geometry
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Proc. Amer. Math. Soc. 131 (2003), 2129-2131 Request permission

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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