Revision as of 00:39, 22 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Prove that the finite dimensional <math>C^*</math>-algebras are exactly the direct sums of matrix algebras <math display="block"> A=M_{N_1}(\mathbb C)\oplus\ldots\oplus M_{N_k}(\mathbb C) </math> by decomposing fi...")
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Apr 22'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Prove that the finite dimensional [math]C^*[/math]-algebras are exactly the direct sums of matrix algebras
[[math]]
A=M_{N_1}(\mathbb C)\oplus\ldots\oplus M_{N_k}(\mathbb C)
[[/math]]
by decomposing first the unit into a sum of central minimal projections.