A finiteness result for commuting squares of matrix algebras

Details A finiteness result for commuting squares of matrix algebras A finiteness result for commuting squares of matrix algebras

2004-04-16

arxiv.org/abs/math/0404301v1

Mathematics

Operator Algebras

Scientific paper

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 $n$-dimensional standard spin models is shown to be satisfied if and only if $n$ 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.

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