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Description

The notion of discrete inclusion of von Neumann factors generalizes the inclusion of a factor into the crossed product by an outer action of a discrete (quantum) group. One can define the standard invariant by generalizing the finite index case. Many examples of abstract standard invariants arise from homogeneous spaces of compact quantum groups. A basic question in this setting is: given an abstract standard invariant and a II1 factor M, can we realize this standard invariant by a discrete subfactor? In this talk, we will introduce an obstruction to realization in terms of the fundamental group of M, and calculate this obstruction for subfactors of Temperley-Lieb-Jones / SU-q(2) type by computing the standard invariant of the centralizer of the canonical state. Based on Joint work with Emily McGovern