Ideal Structure of Nica-Toeplitz Algebras

We study the gauge-invariant ideal structure of the Nica-Toeplitz algebra NT(X) N T ( X ) of a product system ( A , X ) over Nⁿ N n . We obtain a clear description of X -invariant ideals in A , that is, restrictions of gauge-invariant ideals in N-1.111ptT(X) N T ( X ) to A . The main result is a classification of gauge-invariant ideals in N-1.111ptT(X) N T ( X ) for a proper product system in terms of families of ideals in A . We also apply our results to higher-rank graphs.