Doubly Lambda-commuting row isometries, universal models, and classification

摘要

The goal of the paper is to study the structure of the k-tuples of doubly Lambda-commuting row isometries and the C*-algebras they generate from the point of view of noncommutative multivariable operator theory. We obtain Wold decompositions, in this setting, and use them to classify the k-tuples of doubly Lambda-commuting row isometries up to a unitary equivalence. We prove that there is a one-to-one correspondence between the unitary equivalence classes of k-tuples of doubly Lambda-commuting row isometries and the enumerations of 2(k) unitary equivalence classes of unital representations of the twisted Lambda-tensor algebras circle times(Lambda)(i is an element of Ac) O-ni, as A is any subset of {1, ..., k}, where O-ni is the Cuntz algebra with n(i) generators. In addition, we obtain a description and parametrization of the irreducible k-tuples of doubly Lambda-commuting row isometries.