SINGULAR PROJECTION NESTS IN UHF C-STAR-ALGEBRAS

A projection nest in a C*-algebra is said to be singular if the normaliser of its generated C*-algebra is trivial. Uncountably many pairwise nonconjugate singular homogeneous nests are identified (in a given UHF C*-algebra) all of which have the same binary relation invariant. The constructions are based upon (homogeneous) direct systems of upper triangular matrix algebras with rapidly increasing multiplicities and irregular embeddings.