A finiteness result for commuting squares of matrix algebras
arXiv:math/0404301
Abstract
We consider a condition for non-degenerate commuting squares of matrix algebras (finite dimensional von Neumann algebras) called the \emph{span condition}, which in the case of the -dimensional standard spin models is shown to be satisfied if and only if is prime. We prove that the commuting squares satisfying the span condition are isolated among all commuting squares (modulo isomorphisms). In particular, they are finiteley many for any fixed dimension. Also, we give a conceptual proof of previous constructions of certain one-parameter families of biunitaries.