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

We study the universal C^*-algebras generated by n projections $p_1, >..., p_n$ subject to the relation $p_1+... p_n = λ1$, $λ\in \mathbb R$. The questions of when these C^*-algebras are type I, nuclear or exact are considered. It is proved also that among these algebras there is continuum of mutually nonisomorphic ones.

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