On universal 𝐶*-algebras generated by 𝑛 projections with scalar sum

Shulman, Tatiana

doi:10.1090/S0002-9939-08-09654-8

On universal $C^*$-algebras generated by $n$ projections with scalar sum
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Proc. Amer. Math. Soc. 137 (2009), 115-122 Request permission

Abstract:

We study the universal $C^*$-algebras generated by $n$ projections $p_1,\dotsc ,p_n$ subject to the relation $p_1+\cdots +p_n=\lambda 1$, $\lambda \in \mathbb {R}$. The questions of when these $C^*$-algebras are type I, nuclear or exact are considered. It is proved also that among these $C^*$-algebras there is a continuum of mutually nonisomorphic ones.

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