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