The analytic rank of a 𝐶*-algebra

Murphy, Gerard J.

doi:10.1090/S0002-9939-1992-1081095-7

The analytic rank of a $C^ *$-algebra
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by Gerard J. Murphy

Proc. Amer. Math. Soc. 115 (1992), 741-746

DOI: https://doi.org/10.1090/S0002-9939-1992-1081095-7

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Abstract:

A concept of rank for unital ${C^*}$-algebras, which reduces to the dimension of the spectrum in the case of separable abelian ${C^*}$-algebras, is introduced. This rank has properties somewhat similar to the stable rank, but it appears to be easier to compute in many cases. It is very well behaved with respect to tensor products and crossed products with countable discrete abelian groups.

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